This document describes a student project analyzing normal and tangential coordinates through the design and construction of a scale model car track. The objectives are to design a track to determine a model car's travel time, obtain data from the model, and verify results with error calculation tables. Materials and equipment for the track include wood, nails, a flexometer, and model car. The theoretical framework section covers curved motion, normal and tangential coordinates and their applications to situations like a turning car. It describes position, acceleration, and their normal and tangential components. The design, assembly, and testing procedures are outlined. Calculations of parameters, errors, and specific values for the scenario are presented.
Cinemática de partículas en coordenadas normal y tangencial JavierCasa6
This document presents a student project to build a model that simulates curvilinear motion in normal and tangential coordinates. The objectives are to analyze experimental measurements over time, relate calculation errors to experimental data, and estimate the validity of the model. The theoretical framework discusses kinematic elements like particles, reference systems, and uniform circular motion. The procedures and materials used to build the model are presented, along with calculation tables analyzing variables like time, velocity, and length. Calculated errors were below 0.4062%, validating the model. Recommendations include ensuring materials are in good condition and taking precise data measurements with an assistant.
This document provides an overview of planar kinematics of rigid body motion. It describes three types of planar rigid body motion: translation, rotation about a fixed axis, and general plane motion. Translation can be rectilinear or curvilinear. Rotation about a fixed axis involves angular position, velocity, acceleration, and the motion of a point on the rotating body. General plane motion is a combination of translation and rotation. Formulas are provided for analyzing velocity and acceleration during these different types of motion. Examples are also given to demonstrate how to apply the kinematic equations.
This document discusses curvilinear motion of particles. It defines curvilinear motion as motion along a curved trajectory. It also discusses vector analysis of planar curvilinear motion and how it applies to different coordinate systems. Key concepts covered include definitions of displacement, distance, velocity, and acceleration vectors and how their derivatives relate to changes in position, time, and speed during curvilinear motion.
This document discusses circular motion and its key components. It covers:
1) Circular motion involves an object moving along a circular path, which can be described using angular position, velocity, and acceleration instead of linear measurements.
2) The relationships between angular and linear measurements are defined, such as how angular velocity relates to tangential linear velocity.
3) Uniform circular motion and uniformly accelerated circular motion are analyzed, with equations provided for how to calculate variables like displacement given velocity or acceleration.
4) The components of acceleration are described as normal (perpendicular to the path) and tangential, with equations for each in terms of angular acceleration.
This document summarizes key topics in linear motion including:
1) Linear motion concepts like position, displacement, velocity, and acceleration are discussed. Different reference systems are also introduced.
2) Equations for displacement, velocity, and acceleration are provided including how to calculate these values using derivatives of position over time.
3) Specific linear motion examples like uniform and non-uniform accelerated motion are examined along with example problems.
The document describes an experimental analysis of normal and tangential motion coordinates by constructing a prototype to determine the physical components of circular motion. Time was measured over 10 revolutions to analyze tangential and normal acceleration resulting from decomposition of acceleration in circular motion. Error analysis found the average error to be 0.89%, indicating most time measurements were reliable for studying kinematics concepts like tangential and normal coordinates in curvilinear and accelerated circular motion.
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
1. The document outlines the day's objectives of describing rigid body velocity in terms of translation and rotation components, and performing relative motion velocity analysis of points on rigid bodies.
2. It includes examples of applying the concepts to solve problems involving planar motion of links and gears, using the relative velocity equation vB = vA + ω x rB/A.
3. Key steps in the analysis are establishing coordinate systems, drawing kinematic diagrams, expressing velocity vectors in terms of components, and solving the relative velocity equation for unknowns like angular velocity.
Cinemática de partículas en coordenadas normal y tangencial JavierCasa6
This document presents a student project to build a model that simulates curvilinear motion in normal and tangential coordinates. The objectives are to analyze experimental measurements over time, relate calculation errors to experimental data, and estimate the validity of the model. The theoretical framework discusses kinematic elements like particles, reference systems, and uniform circular motion. The procedures and materials used to build the model are presented, along with calculation tables analyzing variables like time, velocity, and length. Calculated errors were below 0.4062%, validating the model. Recommendations include ensuring materials are in good condition and taking precise data measurements with an assistant.
This document provides an overview of planar kinematics of rigid body motion. It describes three types of planar rigid body motion: translation, rotation about a fixed axis, and general plane motion. Translation can be rectilinear or curvilinear. Rotation about a fixed axis involves angular position, velocity, acceleration, and the motion of a point on the rotating body. General plane motion is a combination of translation and rotation. Formulas are provided for analyzing velocity and acceleration during these different types of motion. Examples are also given to demonstrate how to apply the kinematic equations.
This document discusses curvilinear motion of particles. It defines curvilinear motion as motion along a curved trajectory. It also discusses vector analysis of planar curvilinear motion and how it applies to different coordinate systems. Key concepts covered include definitions of displacement, distance, velocity, and acceleration vectors and how their derivatives relate to changes in position, time, and speed during curvilinear motion.
This document discusses circular motion and its key components. It covers:
1) Circular motion involves an object moving along a circular path, which can be described using angular position, velocity, and acceleration instead of linear measurements.
2) The relationships between angular and linear measurements are defined, such as how angular velocity relates to tangential linear velocity.
3) Uniform circular motion and uniformly accelerated circular motion are analyzed, with equations provided for how to calculate variables like displacement given velocity or acceleration.
4) The components of acceleration are described as normal (perpendicular to the path) and tangential, with equations for each in terms of angular acceleration.
This document summarizes key topics in linear motion including:
1) Linear motion concepts like position, displacement, velocity, and acceleration are discussed. Different reference systems are also introduced.
2) Equations for displacement, velocity, and acceleration are provided including how to calculate these values using derivatives of position over time.
3) Specific linear motion examples like uniform and non-uniform accelerated motion are examined along with example problems.
The document describes an experimental analysis of normal and tangential motion coordinates by constructing a prototype to determine the physical components of circular motion. Time was measured over 10 revolutions to analyze tangential and normal acceleration resulting from decomposition of acceleration in circular motion. Error analysis found the average error to be 0.89%, indicating most time measurements were reliable for studying kinematics concepts like tangential and normal coordinates in curvilinear and accelerated circular motion.
Ekeeda Provides Online Civil Engineering Degree Subjects Courses, Video Lectures for All Engineering Universities. Video Tutorials Covers Subjects of Mechanical Engineering Degree.
1. The document outlines the day's objectives of describing rigid body velocity in terms of translation and rotation components, and performing relative motion velocity analysis of points on rigid bodies.
2. It includes examples of applying the concepts to solve problems involving planar motion of links and gears, using the relative velocity equation vB = vA + ω x rB/A.
3. Key steps in the analysis are establishing coordinate systems, drawing kinematic diagrams, expressing velocity vectors in terms of components, and solving the relative velocity equation for unknowns like angular velocity.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document discusses kinematics, which is the geometry of motion without considering forces. It defines key concepts like displacement, velocity, acceleration, and their relationships. It presents four kinematic equations and provides examples of using these equations and graphs of position-time and velocity-time to solve kinematics problems for objects undergoing uniform and non-uniform acceleration.
This document provides an overview of kinematics of rectilinear motion. It defines key concepts like displacement, distance, speed, velocity, acceleration. It describes equations for uniform and accelerated rectilinear motion as well as vertical motion. It discusses using position-time, velocity-time and acceleration-time graphs to represent rectilinear motion and determine values like displacement, velocity and acceleration. Sample problems are provided to demonstrate applying the concepts and equations.
Kinematics is the study of linear motion. Key terms include displacement, velocity, and acceleration. Displacement is the distance from a starting point, velocity is speed in a direction, and acceleration is the rate of change of velocity. Average values are calculated by total distance or displacement over total time. Instantaneous values give a clearer picture of motion at a moment in time and can be derived from graphs of displacement, velocity, and acceleration over time. When acceleration is constant, five equations can be used to describe motion with constant acceleration.
This document describes a project to design and build a model that demonstrates kinematics in tangential and normal coordinates. The student aims to apply error calculations, analyze physical variables like position, velocity, and acceleration, and construct the equation that defines the particle's trajectory. Experimental data is collected from the model over 10 trials and calculations are shown to determine values like final position, velocity, and accelerations (normal, centrifugal, tangential, and total). Conclusions state that the model successfully analyzed the tangential and normal components of motion and applied error theory to determine average revolutions. Characteristics distinguishing uniform and accelerated circular motion are also described.
This document provides an introduction to linear kinematics. It discusses key linear kinematic variables like distance, displacement, speed, velocity, and acceleration. It defines these variables and the units used to measure them. It also describes the difference between scalar and vector quantities as they relate to motion. Examples of single-point and multi-segment models for describing motion are provided. Equations for calculating speed, velocity, and acceleration from changes in distance, displacement, and time are shown. Projectile motion is also summarized, including the independent vertical and horizontal components of projectile motion.
Chapter 12 kinematics of a particle part-iSajid Yasin
This document provides information about a dynamics course, including:
- The instructor is Engr. Sajid Yasin from the Department of Mechanical Technology at MNS UET Multan.
- Lecture times are Tuesday from 7:30-9:30 PM in Room F5 and Wednesday lab from 6:30-9:30 PM in D2.
- Required textbooks and the method of assessment including exams, quizzes, assignments, and attendance are listed.
This document provides an introduction to kinematics, which is the branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the causes of motion. It covers topics such as scalars and vectors, position and displacement, velocity, acceleration, linear motion, and circular motion. Key concepts discussed include the definitions of displacement, velocity, acceleration, and their relationships. Equations of motion for uniformly accelerated linear and circular motion are also presented.
The document discusses key concepts related to circular motion including:
- Circular motion is defined as motion along a circular path or trajectory.
- Position, velocity, and acceleration in circular motion are described using angular quantities like angular position (θ), angular velocity (ω), and angular acceleration (α).
- Uniform circular motion occurs when the angular velocity ω is constant, resulting in zero angular acceleration.
- Formulas are provided relating angular position, velocity, acceleration, and other variables like time, radius, and frequency for circular motion problems.
Curvilinear motion occurs when a particle moves along a curved path.
Since this path is often described in three dimensions, vector analysis will
be used to formulate the particle's position, velocity, and acceleration
Physics 504 Chapter 9 Uniform Rectilinear MotionNeil MacIntosh
This document discusses uniform rectilinear motion. It defines different types of motion including rectilinear, curvilinear, and random motion. Distance is defined as a scalar quantity representing how far an object has moved, while displacement is a vector quantity that includes both distance and direction. Uniform motion refers to motion at a constant speed in a single direction. Graphs of distance-time and velocity-time relationships are used to analyze motion. The average velocity and speed can be calculated from these graphs by determining slope.
The document discusses uniformly accelerated motion, which is motion where the tangential acceleration is constant. It provides equations that relate the speed, distance, and acceleration of an object undergoing uniformly accelerated motion. Specifically, the speed and distance after a period of time can be determined based on the initial speed, acceleration, and time. The document also discusses applying these concepts to rigid bodies undergoing translational or rotational motion as well as the specific formulas for average acceleration and displacement.
This document discusses the design and construction of a demonstrative equipment for kinematics in normal and tangential coordinates. It describes how the equipment works using a motor, transistor, potentiometer and power source to control the rpm of the motor. Experimental measurements were taken of rpm, angular velocity, angular acceleration and linear velocity. Calculations were performed to determine the average, absolute error, relative error and percentage error of the measurements. The conclusions indicate that experimental error theory can be applied to measurements in normal and tangential coordinates and relate the experimental data to error calculations.
This document discusses the kinematics of particles in rectilinear and curvilinear motion. It defines key concepts like position, displacement, velocity, and acceleration for both continuous and erratic rectilinear motion. Examples are provided to demonstrate how to construct velocity-time and acceleration-time graphs from a given position-time graph, and vice versa. The chapter then discusses general curvilinear motion, defining position, displacement, velocity, and acceleration using vector analysis since the curved path is three-dimensional. Fundamental problems and practice problems are also included.
1) The document describes curvilinear motion and how to analyze the motion of objects moving along curved paths using rectangular components.
2) It provides examples of how to determine the velocity and acceleration of planes in formation and a roller coaster car moving along a fixed helical path using their x, y, and z coordinates.
3) The document also gives an example problem solving for the collision point and speeds of two particles moving along curved paths given their position vectors as functions of time.
This document contains lecture materials on engineering dynamics. It discusses kinematics concepts such as position, velocity, acceleration and their relationships. Rectilinear particle motion is analyzed using graphical and analytical methods. An example problem demonstrates applying kinematics equations to determine the velocity and time taken for a particle to travel between two points under varying acceleration. The document also discusses using graphical methods to analyze erratic or non-uniform particle motion by constructing velocity-time and acceleration-time graphs from a given position-time graph.
The document provides information on seismic cone penetration testing (SCPT), including:
1) SCPT allows for continuous profiling of soil strength (qc), sleeve friction (fs), pore pressure (u), and shear wave velocity (Vs), providing a direct measure of small-strain soil stiffness.
2) Vs is used to estimate fundamental soil parameters like small-strain shear modulus (Go), peak friction angle, and undrained shear strength, and to evaluate soil liquefaction potential.
3) While most research focuses on young uncemented soils, SCPT can also help characterize "unusual" soils like stiff fissured clays, soft rock, and man-made soils that are under-represented
This document discusses free-fall motion and describes an experiment to measure the acceleration due to gravity using a photogate and falling object. The experiment involves dropping an object through a photogate multiple times to collect displacement and time data. Students will then analyze the velocity-time graph to determine the acceleration for each trial and calculate the percent error compared to the accepted value of 9.8 m/s^2. The goal is to perform analysis of free-fall motion and enable students to solve problems involving falling objects.
Physics 504 Chapter 10 Uniformly Accelerated Rectilinear MotionNeil MacIntosh
This document discusses uniformly accelerated rectilinear motion. It introduces kinematics, which is the study of motion without considering causes, and kinetics, which considers the forces that cause motion. Rectilinear motion refers to motion along a straight line, while curvilinear motion is along a curved path. Formulas are provided for calculating final velocity, distance, and acceleration from gravity for vertical motion. Sample problems demonstrate applying the formulas to problems involving projectile motion.
The document discusses concepts related to motion including speed, velocity, acceleration, and free fall. It defines key terms, provides examples of calculating speed, acceleration, and distance using formulas like the relationship between velocity and acceleration under gravity. Examples include calculating the impact speed of cars moving in the same direction and the acceleration and distance traveled by objects in free fall.
Diseño y construccion de una maquina en coordenadas normales y tangenciales s...MARCUSBENJAMINSALINA
This document describes a project to design and build a machine that generates dynamics in normal and tangential coordinates as applied to an automotive engineering physics course. It includes sections on introduction, tools and methods, procedures for use, operation and data collection, discussion and results. The project involves building a ramp structure out of wood with a carton surface to roll a tennis ball down and collect timing and position data to calculate values like normal and tangential acceleration, velocity and radius of curvature.
Diseño y construccion de maqueta en coordendas normales y tangenciales sanche...MATEOSEBASTIANSANCHE
The document describes the design and construction of a model to analyze normal and tangential coordinates through building a car track. The objectives are to design a track to determine a toy car's time, obtain data from the model, and verify results with error calculation tables. Materials used include cardboard, string, scissors, a toy car, ruler, and glue. Equations of motion, normal and tangential coordinates, and velocity and acceleration components are explained. Diagrams show the model's assembly, and conclusions state that measurements and instruments must be accurate to obtain useful data for calculations. Recommendations include verifying data, using necessary elements, and considering designs.
The document summarizes key concepts from Chapter 2 of a Physics textbook on kinematics of linear motion. It discusses the following in 3 sentences:
Linear motion can be one-dimensional or two-dimensional projectile motion. Equations of motion include relationships between displacement, velocity, acceleration, and time. Uniformly accelerated motion follows equations that relate the initial and final velocity, acceleration, and time to determine displacement and distance traveled.
This document discusses kinematics, which is the geometry of motion without considering forces. It defines key concepts like displacement, velocity, acceleration, and their relationships. It presents four kinematic equations and provides examples of using these equations and graphs of position-time and velocity-time to solve kinematics problems for objects undergoing uniform and non-uniform acceleration.
This document provides an overview of kinematics of rectilinear motion. It defines key concepts like displacement, distance, speed, velocity, acceleration. It describes equations for uniform and accelerated rectilinear motion as well as vertical motion. It discusses using position-time, velocity-time and acceleration-time graphs to represent rectilinear motion and determine values like displacement, velocity and acceleration. Sample problems are provided to demonstrate applying the concepts and equations.
Kinematics is the study of linear motion. Key terms include displacement, velocity, and acceleration. Displacement is the distance from a starting point, velocity is speed in a direction, and acceleration is the rate of change of velocity. Average values are calculated by total distance or displacement over total time. Instantaneous values give a clearer picture of motion at a moment in time and can be derived from graphs of displacement, velocity, and acceleration over time. When acceleration is constant, five equations can be used to describe motion with constant acceleration.
This document describes a project to design and build a model that demonstrates kinematics in tangential and normal coordinates. The student aims to apply error calculations, analyze physical variables like position, velocity, and acceleration, and construct the equation that defines the particle's trajectory. Experimental data is collected from the model over 10 trials and calculations are shown to determine values like final position, velocity, and accelerations (normal, centrifugal, tangential, and total). Conclusions state that the model successfully analyzed the tangential and normal components of motion and applied error theory to determine average revolutions. Characteristics distinguishing uniform and accelerated circular motion are also described.
This document provides an introduction to linear kinematics. It discusses key linear kinematic variables like distance, displacement, speed, velocity, and acceleration. It defines these variables and the units used to measure them. It also describes the difference between scalar and vector quantities as they relate to motion. Examples of single-point and multi-segment models for describing motion are provided. Equations for calculating speed, velocity, and acceleration from changes in distance, displacement, and time are shown. Projectile motion is also summarized, including the independent vertical and horizontal components of projectile motion.
Chapter 12 kinematics of a particle part-iSajid Yasin
This document provides information about a dynamics course, including:
- The instructor is Engr. Sajid Yasin from the Department of Mechanical Technology at MNS UET Multan.
- Lecture times are Tuesday from 7:30-9:30 PM in Room F5 and Wednesday lab from 6:30-9:30 PM in D2.
- Required textbooks and the method of assessment including exams, quizzes, assignments, and attendance are listed.
This document provides an introduction to kinematics, which is the branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the causes of motion. It covers topics such as scalars and vectors, position and displacement, velocity, acceleration, linear motion, and circular motion. Key concepts discussed include the definitions of displacement, velocity, acceleration, and their relationships. Equations of motion for uniformly accelerated linear and circular motion are also presented.
The document discusses key concepts related to circular motion including:
- Circular motion is defined as motion along a circular path or trajectory.
- Position, velocity, and acceleration in circular motion are described using angular quantities like angular position (θ), angular velocity (ω), and angular acceleration (α).
- Uniform circular motion occurs when the angular velocity ω is constant, resulting in zero angular acceleration.
- Formulas are provided relating angular position, velocity, acceleration, and other variables like time, radius, and frequency for circular motion problems.
Curvilinear motion occurs when a particle moves along a curved path.
Since this path is often described in three dimensions, vector analysis will
be used to formulate the particle's position, velocity, and acceleration
Physics 504 Chapter 9 Uniform Rectilinear MotionNeil MacIntosh
This document discusses uniform rectilinear motion. It defines different types of motion including rectilinear, curvilinear, and random motion. Distance is defined as a scalar quantity representing how far an object has moved, while displacement is a vector quantity that includes both distance and direction. Uniform motion refers to motion at a constant speed in a single direction. Graphs of distance-time and velocity-time relationships are used to analyze motion. The average velocity and speed can be calculated from these graphs by determining slope.
The document discusses uniformly accelerated motion, which is motion where the tangential acceleration is constant. It provides equations that relate the speed, distance, and acceleration of an object undergoing uniformly accelerated motion. Specifically, the speed and distance after a period of time can be determined based on the initial speed, acceleration, and time. The document also discusses applying these concepts to rigid bodies undergoing translational or rotational motion as well as the specific formulas for average acceleration and displacement.
This document discusses the design and construction of a demonstrative equipment for kinematics in normal and tangential coordinates. It describes how the equipment works using a motor, transistor, potentiometer and power source to control the rpm of the motor. Experimental measurements were taken of rpm, angular velocity, angular acceleration and linear velocity. Calculations were performed to determine the average, absolute error, relative error and percentage error of the measurements. The conclusions indicate that experimental error theory can be applied to measurements in normal and tangential coordinates and relate the experimental data to error calculations.
This document discusses the kinematics of particles in rectilinear and curvilinear motion. It defines key concepts like position, displacement, velocity, and acceleration for both continuous and erratic rectilinear motion. Examples are provided to demonstrate how to construct velocity-time and acceleration-time graphs from a given position-time graph, and vice versa. The chapter then discusses general curvilinear motion, defining position, displacement, velocity, and acceleration using vector analysis since the curved path is three-dimensional. Fundamental problems and practice problems are also included.
1) The document describes curvilinear motion and how to analyze the motion of objects moving along curved paths using rectangular components.
2) It provides examples of how to determine the velocity and acceleration of planes in formation and a roller coaster car moving along a fixed helical path using their x, y, and z coordinates.
3) The document also gives an example problem solving for the collision point and speeds of two particles moving along curved paths given their position vectors as functions of time.
This document contains lecture materials on engineering dynamics. It discusses kinematics concepts such as position, velocity, acceleration and their relationships. Rectilinear particle motion is analyzed using graphical and analytical methods. An example problem demonstrates applying kinematics equations to determine the velocity and time taken for a particle to travel between two points under varying acceleration. The document also discusses using graphical methods to analyze erratic or non-uniform particle motion by constructing velocity-time and acceleration-time graphs from a given position-time graph.
The document provides information on seismic cone penetration testing (SCPT), including:
1) SCPT allows for continuous profiling of soil strength (qc), sleeve friction (fs), pore pressure (u), and shear wave velocity (Vs), providing a direct measure of small-strain soil stiffness.
2) Vs is used to estimate fundamental soil parameters like small-strain shear modulus (Go), peak friction angle, and undrained shear strength, and to evaluate soil liquefaction potential.
3) While most research focuses on young uncemented soils, SCPT can also help characterize "unusual" soils like stiff fissured clays, soft rock, and man-made soils that are under-represented
This document discusses free-fall motion and describes an experiment to measure the acceleration due to gravity using a photogate and falling object. The experiment involves dropping an object through a photogate multiple times to collect displacement and time data. Students will then analyze the velocity-time graph to determine the acceleration for each trial and calculate the percent error compared to the accepted value of 9.8 m/s^2. The goal is to perform analysis of free-fall motion and enable students to solve problems involving falling objects.
Physics 504 Chapter 10 Uniformly Accelerated Rectilinear MotionNeil MacIntosh
This document discusses uniformly accelerated rectilinear motion. It introduces kinematics, which is the study of motion without considering causes, and kinetics, which considers the forces that cause motion. Rectilinear motion refers to motion along a straight line, while curvilinear motion is along a curved path. Formulas are provided for calculating final velocity, distance, and acceleration from gravity for vertical motion. Sample problems demonstrate applying the formulas to problems involving projectile motion.
The document discusses concepts related to motion including speed, velocity, acceleration, and free fall. It defines key terms, provides examples of calculating speed, acceleration, and distance using formulas like the relationship between velocity and acceleration under gravity. Examples include calculating the impact speed of cars moving in the same direction and the acceleration and distance traveled by objects in free fall.
Diseño y construccion de una maquina en coordenadas normales y tangenciales s...MARCUSBENJAMINSALINA
This document describes a project to design and build a machine that generates dynamics in normal and tangential coordinates as applied to an automotive engineering physics course. It includes sections on introduction, tools and methods, procedures for use, operation and data collection, discussion and results. The project involves building a ramp structure out of wood with a carton surface to roll a tennis ball down and collect timing and position data to calculate values like normal and tangential acceleration, velocity and radius of curvature.
Diseño y construccion de maqueta en coordendas normales y tangenciales sanche...MATEOSEBASTIANSANCHE
The document describes the design and construction of a model to analyze normal and tangential coordinates through building a car track. The objectives are to design a track to determine a toy car's time, obtain data from the model, and verify results with error calculation tables. Materials used include cardboard, string, scissors, a toy car, ruler, and glue. Equations of motion, normal and tangential coordinates, and velocity and acceleration components are explained. Diagrams show the model's assembly, and conclusions state that measurements and instruments must be accurate to obtain useful data for calculations. Recommendations include verifying data, using necessary elements, and considering designs.
This document discusses the objectives, materials, and work involved in analyzing normal and tangential coordinates through the design and construction of a scale model car track. The general objective is to analyze the components of normal and tangential coordinates. Specific objectives include designing a track to determine the car's travel time, obtaining data from the model, and verifying results with error calculations based on time. Materials for the track include cardboard, wood tubes, glue, and a small metal car. The work involves preparing the design, construction, obtaining data, and error analysis calculations.
Movimiento circular uniforme aplicado a la maqueta de un ventiladorAlexToavanda
The document describes the design and construction of a model that demonstrates circular uniform motion (MCU). The objectives are to build a model that determines the time it takes to complete 10 revolutions. Equipment and materials used include cardboard, a compass, ruler, pencil, cutter, glue gun, DC motor, and power adapter. The procedure to build the model is described. Data on time to complete 10 revolutions is collected and calculations are done to determine the average, absolute error, relative error, and validity of data values. The conclusions drawn are that the model helps understand curvilinear motion and error analysis verifies data precision. Recommendations include verifying calculations and improving time measurement precision.
Diapositivas_Construcción de Máquina de Movimiento Perpetuo_Zea PaulPaulAndresZeaLarrea
This document describes a student project to design and construct a perpetual motion machine. It provides background context on previous attempts at building perpetual motion machines. The student's objectives are to build a machine that can run continuously for at least 10 minutes. The document outlines the materials that will be used, theoretical concepts regarding energy and thermodynamics, procedures for design, assembly, calibration and error analysis, and results from testing different machine configurations. The best design was able to run for 10 minutes and 36.96 seconds.
1. The document outlines a student fieldwork report on traversing, which is a surveying technique used to establish positions of points and features on land.
2. It describes the process of measuring angles and distances between stations using a theodolite and other equipment, and calculating latitudes, departures, and station coordinates.
3. The results found the total error to be within an acceptable accuracy level, showing the traverse was successful in establishing the relative positions of points to the required precision.
This document describes a closed traverse survey conducted by a group of students. It includes an introduction to traversing, the equipment used (theodolite, tripod, leveling rods), field data collection methods, calculations of angular errors, distances, azimuths, latitudes and departures, and station coordinates. The group adjusted their results based on the Compass Rule correction and achieved an accuracy of 1:1088 for the closed traverse. They discussed lessons learned from conducting the fieldwork.
Toyota Kata How to Use the Key Improvement Kata FormsRichardCGreen
The standard Improvement Kata / Coaching Kata forms in this SlideShare help you operationalize the IK/CK patterns in your organization. They are being used by Kata practitioners worldwide, and within the A3 format
This document provides an introduction to traversing and closed traverse techniques. It discusses the components of a closed traverse including loop and connecting traverses. It outlines the proper selection of traverse stations and defines azimuths, bearings, and acceptable misclosures. The document also describes the equipment used for traversing, including a theodolite, tripod stand, optical plummet, and spirit bubble. It states the objectives, discusses the fieldwork process, and concludes that the student team was able to obtain accurate angle readings to complete the closed traverse.
This document is an 18 page site surveying report for a traversing fieldwork exercise. It includes an introduction to traversing, objectives, descriptions of surveying equipment used, raw field data collected, adjustments made to account for angular errors, calculations of bearings, latitudes, and departures, and station coordinates. The report discusses setting up the equipment, challenges faced, and concludes the angles were adjusted to equal 360 degrees and coordinates were determined within the required accuracy standards.
This document is a site surveying report for a traversing fieldwork exercise. It includes an introduction to traversing, objectives of the exercise, descriptions of surveying equipment used like theodolites and ranging rods. Data collected in the field including angular measurements, bearings, latitudes and departures are presented. The results show angular errors requiring adjustment of field angles. Station coordinates are tabulated and graphed. The conclusion is that adjustments were needed to correct angular errors and produce accurate coordinate data from the traversing exercise.
Dinámica en coordenadas normales y tangenciales-Presentación WILMERMAURICIOSOSADI
The document describes the construction of a model that demonstrates normal and tangential coordinates in dynamics. It includes objectives, materials used, assembly procedures, utilization procedures, and calculations of parameters like velocity, acceleration, and error. A rotating platform is built and attached to a spring and mass to measure changes in RPM over time. Measurements are taken over 10 trials and averaged to calculate absolute and relative errors of less than 1%.
Improving the Hydraulic Efficiency of Centrifugal Pumps through Computational...IJERA Editor
The design and optimization of turbo machine impellers such as those in pumps and turbines is a highly complicated task due to the complex three-dimensional shape of the impeller blades and surrounding devices. Small differences in geometry can lead to significant changes in the performance of these machines. We report here an efficient numerical technique that automatically optimizes the geometry of these blades for maximum performance. The technique combines, mathematical modeling of the impeller blades using non-uniform rational B-spline (NURBS), Computational fluid dynamics (CFD) with Geometry Parameterizations in turbulent flow simulation and the Globalized and bounded Nelder-Mead (GBNM) algorithm in geometry optimization.
The document summarizes a student's fieldwork using a theodolite to conduct a traversing survey. Key details include:
- The student conducted a closed traverse survey with 4 stations, measuring angles and lengths between stations.
- Angular errors were distributed and angles were adjusted to total 360°. Station coordinates were then computed.
- Total angular error was -0°12'20" and total linear error was 0.0668m, yielding an accuracy of 1:2700, within acceptable limits.
- The fieldwork helped students learn skills like setting up a theodolite, measuring angles and distances, and adjusting data.
This document summarizes the implementation of a quadcopter with live video monitoring. It discusses the structure of the quadcopter, including its mechanical and electronic components. It also describes the SolidWorks design, MATLAB simulation, control theory using PID controllers, and sensor fusion techniques. The goal is to develop a stable quadcopter that can be flown wirelessly from a distance while transmitting live video footage. Future work may focus on more complex autonomous flight routines and swarm coordination.
Report Assignment 2 for Site Surveying module which requires us to do Traversing measurement around the campus carpark, for the Bachelor of Quantity Surveying (BQS) Course Semester 2, Taylor's University Lakeside Campus
This document presents the unadjusted field data, calculations, and results from three traverses conducted as part of a surveying fieldwork assignment. It includes the raw field measurements, average values, angular error calculations, bearing and azimuth determinations, latitudes and departures, station coordinate tables and graphs. The document aims to provide students with hands-on experience in traversing techniques and data processing.
This document describes an experiment on the dynamics of machines lab at Ideal Institute of Technology. It provides instructions on how to perform experiments on slider crank mechanisms and cams. The objectives, apparatus, theory, procedures, observations tables, calculations, graphs, results and discussions are outlined for experiments 1 and 2 on the slider crank mechanism and cams respectively. Precautions and potential sources of error are also noted.
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Diapositivas coordenadas normales y tangenciales camila quinteros
1. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
UNIVERSIDAD DE LAS FUERZAS ARMADAS ESPE SEDE LATACUNGA
DEPARTAMENTO DE ENERGÍA Y MECÁNICA
CARRERA DE INGENIERÍA AUTOMOTRÍZ
TEMA :
CINEMÁTICA EN COORDENADAS NORMALES Y TANGENCIALES
ESTUDIANTE:
CAMILA QUINTEROS
NRC:
8104
ING:
ING. DIEGO PROAÑO MOLINA MSC.
2. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
OBJETIVOS
Objetivo General:
• Analizar los componentes de las coordenadas normales y tangenciales, mediante
el diseño y construcción de una pista de automóviles considerando las variables
a tomar en cuenta para el cálculo de los datos obtenidos con instrumentos
tecnológicos para comprobar los resultados con las tablas de cálculos de errores.
Objetivos Específicos:
• Diseñar una pista para determinar el tiempo de recorrido del automóvil a escala.
• Obtener datos de la maqueta construida para luego desarrollar los cálculos.
• Comprobar los resultados obtenidos con la tabla de calculo de errores en función
al tiempo
3. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
Material Características Cantidad Código
a) Pleibo de Madera Es de madera y sus dimensiones es( 1m x 50cm) 1 S/N
a)
Tira de MDF Es de Madera y sus dimensiones es( 1cm x) 1 S/N
a) Clavos
Es de metal y delgado 1/2 S/N
a)
Martillo
Objeto eléctrico que sirve para martillar fijamente
1 S/N
a)
Flexómetro
Longitud máxima de Medida 5 m y su grado de
precisión es de 1mm
1 S/N
a)
Compas
Es de madera utilizado para hacer la circunferencia
3 S/N
a) Cortadora
Objeto Eléctrico que sirve para cortar la madera
1 S/N
a)
Lija
Objeto de grano delgado, anguloso, quebradizo y no
mucha durabilidad
2 S/N
a)
Cuerpo de Prueba Un carrito pequeño 1 S/N
EQUIPO Y MATERIALES
Tabla 1. Equipo y Materiales de la Práctica
4. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
Figura N° 1 Equipos y materiales del Diseño de la Maqueta de Coordenadas Normales y Tangenciales
5. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
MARCO TEÓRICO
1. Movimiento Curvilíneo
• El movimiento curvilíneo es cuando una partícula o cuerpo ejecuta un movimiento curvilíneo,
cuando dicha partícula describe una trayectoria que no es recta. [2]
• Por lo general en la naturaleza, así como en la técnica es muy corriente encontrarse con
movimientos cuyas trayectorias no son líneas rectas, sino curvas. Estos movimientos son llamados
curvilíneos, y se encuentran con más frecuencia que los rectilíneos, e incluso existen cuerpos en el
espacio que hacen este tipo de movimiento, por ejemplo: satélites, planetas, etc; de igual manera en
nuestro planeta Tierra como lo son los medios de transportes, maquinas, el aire, partes de
máquinas, el agua que corre por el grifo, etc. [2]
6. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
MARCO TEÓRICO
1.1 Coordenadas Normal y Tangencial.
• Como se puede conocer la velocidad es tangente a la trayectoria, pero la aceleración no lo es, es
por tal motivo que se conoce que la velocidad en magnitud y sentido se desea calcular la
aceleración, para esto se usa un sistema móvil que se acopla a la velocidad en uno de sus ejes. Este
tipo de sistema lleva como nombre normal o tangencial. [3]
Figura 2. Sistema de coordenadas. [4]
7. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
MARCO TEÓRICO
1.2 Aplicaciones
Para aplicar este sistema de coordenadas existen diferentes escenarios para hacerlo como pueden ser:
[5]
• Cuando un auto se mueve en una curva experimenta una aceleración, debido al cambio en la
magnitud o en la dirección de la velocidad. [6]
• Un motociclista inicia su movimiento desde el reposo e incrementa su velocidad a razón constante.
[7]
Figura 3. Ejemplo del motociclista [5]
8. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
MARCO TEÓRICO
1.3 Posición
• Cuando la trayectoria de una partícula es conocida, a veces es conveniente utilizar las coordenadas
normales (n) y tangenciales (t) las cuales actúan en las direcciones normal y tangencial a la
trayectoria. [8]
• En un movimiento plano se utilizan vectores unitarios 𝒖𝒊 y 𝒖𝒏 [9]
• El eje t es tangente a la trayectoria y positivo en la dirección del movimiento y el eje n es
perpendicular al eje t y está dirigido hacia el centro de la curvatura. [10]
Figura 4. Posición. [11]
9. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
MARCO TEÓRICO
1.3 Aceleración
• La aceleración puede descomponerse en una componente tangencial at (aceleración tangencial)
paralela a la tangente y otra paralela a la normal an (aceleración normal), entonces la aceleración
tangencial es responsable del cambio en el módulo de la velocidad y la aceleración normal es la
responsable del cambio en la dirección de la velocidad. [20]
•
Figura 7. Aceleración. [17]
10. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
PROCEDIMIENTO DE DISEÑO
• Analizar los Distintos Diseños que se puede encontrar sobre las Coordenadas Normales y
Tangenciales
• Escoger nuestro Diseño, Bosquejar y definir todo aquello que se pueda calcular sobre el
tema.
• Identificar los Errores del calculo en el diseño escogido
• Realizar el diseño, una vez calculado todos los componentes y errores
11. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
PROCEDIMIENTO DE ARMADO
• Se tomaron las, medidas de la tabla tríplex
• Se realizo el corte con herramientas especializadas en corte liso
• Se diseño la pista y se la procedió a calar en la máquina para diseños curvos
• Se saco una copia con la plantilla principal
• Se corto los amarres de madera para el armado
• Se armo o se unió las plantillas
• Se procedió a lijar y pintar
• Se le dio acabados con colores de papel
Figura 5 Figura 6
12. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
PROCEDIMIENTO DE UTILIZACIÓN
Realización del ensayo:
• Mediante el diseño elaborado se toma el tiempo de partida ( 𝑣0) y tiempo de llegada(1,51) del vehículo
• Tomar en cuenta la distancia recorrida del vehículo, para poder determinar la velocidad alcanzada por el coche
• Luego de encontrar la velocidad alcanzada del vehículo, se debe determinar la aceleración
• La aceleración se la determina por la fórmula de la velocidad sobre el tiempo
• Ya teniendo la aceleración y la velocidad como datos principales del ejercicio, con ello podemos determinar la
aceleración tangencial y normal, aplicando coordenadas en el punto A y en el punto B y aplicar triángulos rectángulos
para aplicar leyes de Seno y Coseno y de esa manera determinamos con cada uno de sus catetos e Hipotenusa los
resultados, con ello tenemos la aceleración tangencial y normal
• Con la aceleración Tangencial se va a encontrar el cateto adyacente y con la aceleración normal se determina mediante
el cateto opuesto
• Estos son los valores obtenidos son principales para determinar la aceleración total
• Con la aceleración normal, también se puede determinar el radio, mediante la formula de velocidad al cuadrado sobre
RO (termino griego) en si es el mismo radio
• Ese radio se lo despeja y se lo multiplica el valor de la aceleración normal con la velocidad al cuadrado
• Se halla la fórmula de posicionamiento para determinar el posicionamiento del Vehículo en el punto B
• Y también se determina la velocidad angular del punto B y el punto A y se toma en cuenta la frecuencia que se mide en
Hercio y el periodo
14. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
CÁLCULOS DE ERRORES
DATOS:
Tabla 2. Parámetros físicos
CÁLCULO DE ERRORES:
Tabla 3. Valor promedio del tiempo
Parámetro físico Dimensión Símbolo Unidades
Radio L r m
Tiempo T t s
Altura L h h
Aceleración LT-2 𝑎
m/s2
Aceleración Normal LT-2 𝑎𝑁 m/s2
Aceleración
Tangencial
LT-2 𝑎𝑡 m/s2
Aceleración Total LT-2 𝑎𝑇 m/s2
Aceleración
Centrifuga
LT-2 𝑎𝑐 m/s2
Velocidad LT-1 𝑣
m/s
Parámetro
físico
Símbolo Dimensión Valor Unidades
Tiempo 1 t1 T 1,51 s
Tiempo 2 t2 T 1,54 s
Tiempo 3 t3 T 1,51 s
Tiempo 4 t4 T 1,55 s
Tiempo 5 t5 T 1,54 s
Tiempo 6 t6 T 1,52 s
Tiempo 7 t7 T 1,51 s
Tiempo 8 t8 T 1,54 s
Tiempo 9 t9 T 1,53 s
Tiempo 10 t10 T 1,55 s
Tiempo 𝑥
1,53
15,3/10
Tabla 4. Valor promedio del tiempo
𝑥 =
𝑖=1
𝑛 𝑥1 + 𝑥2 + 𝑥𝑛
𝑛
15. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
CÁLCULOS DE ERRORES
Tabla 4. Calculo del Error Absoluto
Valor
Valor
Promedio
Error Absoluto
1,51 1,53 0,02
1,54 1,53 0,01
1,51 1,53 0,02
1,55 1,53 0,02
1,54 1,53 0,01
1,52 1,53 0,01
1,51 1,53 0,02
1,54 1,53 0,01
1,53 1,53 0
1,55 1,53 0,02
𝐸𝑎𝑏𝑠𝑖 (Tiempo) 𝐸𝑎𝑏𝑠
0,14/10
0,014
𝑎𝑏𝑠 =
𝑖=1
𝑛 𝐸𝑎𝑏𝑠1 + 𝐸𝑎𝑏𝑠2+𝐸𝑎𝑏𝑠𝑛
𝑛
Tabla 4. Promedio de Error absoluto
𝐸𝑎𝑏𝑠𝑖 = 𝑥 − 𝑥𝑖
16. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
Tiempo
𝐸𝑟 =
𝐸𝑎𝑏𝑠
𝑥
𝐸𝑟 =
0,014
1,53
𝐸𝑟 = 0,00915
Tabla 5. Calculo del Error Relativo
Tiempo
𝑬% = 𝑬𝒓 ∗ 𝟏𝟎𝟎%
𝐸% = 0,00928 ∗ 100%
𝐸% = 0,928%
Tabla 6. Calculo del Error Porcentual
Tiempo
(𝒙 ± 𝑬𝒂𝒃𝒔)
𝑉𝑚𝑖𝑛 = 𝒙 − 𝑬𝒂𝒃𝒔)
𝑉𝑚𝑖𝑛 = (1,53 − 0,014)
𝑉𝑚𝑖𝑛 = 1,51
𝑉𝑚á𝑥 = (𝑥 + 𝐸𝑎𝑏𝑠))
𝑉𝑚á𝑥 = (1,53 + 0,014)
𝑉𝑚á𝑥 = 1,54
Tabla 7. Calculo Rango de Valores
CÁLCULOS DE ERRORES
17. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
CALCULOS RESPECTIVOS
Un Vehículo se desplaza sobre la carretera desde el punto A en un tiempo estimado de 1,51𝑠 en hasta el
punto B a una distancia de 0,83m, siendo el ángulo de 160° del Punto B, y el ángulo de 20° del punto A
Determinar:
a)La velocidad alcanzada en el punto B
b)La aceleración alcanzada desde el punto A hasta el Punto B
c)La componente de aceleración Normal
d)La componente de aceleración Tangencial
e)El Radio de curvatura
f)La aceleración Total
g)El Posicionamiento en el Punto B
h)La velocidad Angular inicial
i)La Velocidad Angular final
j)La frecuencia
k)El Periodo
18. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
RESULTADOS OBTENIDOS
Tabla 8 Resultados Obtenidos
Parámetro físico Dimensión Símbolo Valor Unidades
Radio L
𝑟
2,52 m
Tiempo T
𝑡
1,51 s
Distancia 0,83 m
Aceleración LT-2 𝑎
0,36 m/s2
Aceleración
Normal
LT-2 𝑎𝑁 0,12 m/s2
Aceleración
Tangencial
LT-2 𝑎𝑡 -0,134 m/s2
Aceleración Total LT-2 𝑎𝑇 0,36 m/s2
Posicionamiento LT-2 𝑠
19,95 m/s2
Velocidad LT-1 𝑣 0,55 m/s
Velocidad
Angular Inicial
LT-1 𝜔
13,25 rad/s
Velocidad
Angular Final
LT-1 𝜔
105,96 rad/s
Frecuencia LT-1 𝐹
16,86 Hz
Periodo LT-1 𝑃
0,05 s
19. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
CONCLUSIONES:
• La construcción de la pista se la diseño con la finalidad de obtener datos importantes para desarrollar calculo
matemáticos y poder analizarlos, se considero el tiempo como el primer dato a tomar en cuenta por el hecho que
un dato fácil de obtener y para analizar la velocidad de recorrido del coche.
• Al construir la maqueta se determino las medidas relacionadas a los valores que se iban a obtener para calcular
los datos obtenidos, ya que los cálculos iban de determinar los componentes tangenciales y normales que se
aplicaran en este trabajo desarrollado.
• Ya obtenidos los valores del trabajo se verifico los resultados con la tabla de cálculo de errores que se la utiliza
en estos procesos matemáticos ya que el desarrollo de las comprobaciones deben ser precisas y con esta
comprobación se analiza todos los procesos de datos y resultados que arrojara los ejercicios de calculo
20. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
RECOMENDACIONES:
• Utilizar las herramientas y componentes necesarios para elaborar una maqueta didáctica ya que para
obtener los datos es importante comprobar que este bien diseñada toda la pista con la que se esta
trabajando
• Al obtener los datos se debe revisar que estén bien tomados, para su respetivo calculo y despeje de
formulas, tomando en cuenta los resultados obtenidos para comprobarlos con los que arroja la tabla de
cálculos de errores.
• Considerar importante los planos y diseños que se desarrollan en este trabajo ya que son parte
importante de la demostración y exposición que se llevara a cabo a lo largo del desarrollo del trabajo
realizado
21. FECHA ÚLTIMA REVISIÓN: 09/10/13 CÓDIGO: SGC.DI.260 VERSIÓN: 1.1
REFERENCIAS BIBLIOGRÁFICAS
[1] Arjona. M. (2021). Cinemática de una partícula. <https://es.slideshare.net/Hermelindahhu/cinematica-de-una-particula>. [Consulta: 27 de octubre de 2021]
[2] Bragado, M. I. (2003). Física General. Madrid: Universidad Complutense de Madrid. https://www.ucm.es/data/cont/docs/18-2020-04-15-Ignacio-martin-
bragado.pdf
[3] Cortez. M. (2017). CINEMÁTICA DE UNA PARTÍCULA. https://slideplayer.es/slide/11817133/. [Consulta: 27 de octubre de 2021]
[4] Díaz. F. 2017. Movimiento curvilíneo. https://es.slideshare.net/josueatiliocarballosantamaria/5-unidad-n2-movimiento-curvilineo-parte-ii. [Consulta: 27 de octubre
de 2021]
[5] ECURED. (2021), Movimiento Curvilíneo. <https://www.ecured.cu/Movimiento_curvil%C3%ADneo.> [Consulta: 27 de octubre de 2021]
[6] Franco. G. (2016). Componentes tangencial y normal de la aceleración. Radio de curvatura.
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[7] Pozo. J . (2005). ALGUNOS TÓPICOS Y APLICACIONES DE LA
MECANICA RACIONAL.
https://repositorio.umsa.bo/xmlui/bitstream/handle/123456789/1733/Cap%C3%ADtulo%20I%20(Algunos%20t%C3%B3picos%20de%20Cinem%C3%A1tica).pdf?se
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[8] Gualotuña. L. (2020). Ecuaciones de movimiento: Coordenadas normales y tangenciales. https://en.calameo.com/read/0063505230f8fc0c52790. [Consulta: 27 de
octubre de 2021]
[9] Macho. L. (2019). Componentes normales. https://slideplayer.es/slide/3966575/. [Consulta: 27 de octubre de 2021]
[10] Moron. J. (2019). Movimiento circular y curvilíneo. https://www.scribd.com/document/426167397/MOVIMIENTO-CIRCULAR-Y-CURVILINEO-docx.
[Consulta: 27 de octubre de 2021]