Week 3 OverviewLast week, we covered multiple forces acting on.docxmelbruce90096
Week 3 Overview
Last week, we covered multiple forces acting on an object. This week we will cover motion in two dimensions, inclined planes, circular motion, and rotation.
Forces in Two Dimensions (1 of 2)
So far you have dealt with single forces acting on a body or more than two forces that act parallel to each other. But in real life situations more than one force may act on a body. How are Newton's laws applied to such cases? We will restrict the forces to two dimensions.
Since force and acceleration are vectors, Newton's law can be applied independently to the X and Y-axes of a coordinate system. For a given problem you can choose a suitable coordinate system. But once a coordinate system is chosen, we have to stick with it for that problem. The example that follows shows how to find the acceleration of a body when two forces act on it at right angles to each other.
Forces in Two Dimensions (2 of 2)
To find the resultant acceleration we draw an arrow OA of length 3 units along the X-axis and then an arrow AB of length 4 units along the Y-axis. The resultant acceleration is the arrow OB with the length of 5 units. Therefore, the acceleration is 5 m/s2 in the direction of OB. Also when you measure the angle AOB with a protractor, we find it to be 53°.
The acceleration caused by the two forces is 5 m/s2 at an angle of 53°.
Uniform Circular Motion
When an object travels in a circular path at a constant speed, its motion is referred to as uniform circular motion, and the object is accelerated towards the center of the circle. If the radius of the circular path is r, the magnitude of this acceleration is ac = v2 / r, where v is its speed and ac is called the centripetal acceleration. A centripetal force is responsible for the centripetal acceleration, which constantly pulls the object towards the center of the circular path. There cannot be any circular motion without a centripetal force.
Banking
When there is a sharp turn in the road or when a turn has to be taken at a high speed as in a racetrack, the outer part of the road or the track is raised from the inner part of the track. This is called banking. It provides additional centripetal force to a turning vehicle so that it doesn't skid.
The angle of banking is kept just right so that it provides all the centripetal force required and a motorist does not have to depend on the friction force at all.
Inclined Planes
Forces on an Inclined Plane
The inclined plane is a device that reduces the force needed to lift objects. Consider the forces acting on a block on an inclined surface. The inclined surface exerts a normal force FN on the block that is perpendicular to the incline. The force of gravity, FG, points downward. If there is no friction, the net force, Fnet, acting on the block is the resultant of FN and FG. By Newton's second law the net force must point down the incline because the block moves only along the incline and not perpendicular to it.
The vector triangle shows .
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Week 3 OverviewLast week, we covered multiple forces acting on.docxmelbruce90096
Week 3 Overview
Last week, we covered multiple forces acting on an object. This week we will cover motion in two dimensions, inclined planes, circular motion, and rotation.
Forces in Two Dimensions (1 of 2)
So far you have dealt with single forces acting on a body or more than two forces that act parallel to each other. But in real life situations more than one force may act on a body. How are Newton's laws applied to such cases? We will restrict the forces to two dimensions.
Since force and acceleration are vectors, Newton's law can be applied independently to the X and Y-axes of a coordinate system. For a given problem you can choose a suitable coordinate system. But once a coordinate system is chosen, we have to stick with it for that problem. The example that follows shows how to find the acceleration of a body when two forces act on it at right angles to each other.
Forces in Two Dimensions (2 of 2)
To find the resultant acceleration we draw an arrow OA of length 3 units along the X-axis and then an arrow AB of length 4 units along the Y-axis. The resultant acceleration is the arrow OB with the length of 5 units. Therefore, the acceleration is 5 m/s2 in the direction of OB. Also when you measure the angle AOB with a protractor, we find it to be 53°.
The acceleration caused by the two forces is 5 m/s2 at an angle of 53°.
Uniform Circular Motion
When an object travels in a circular path at a constant speed, its motion is referred to as uniform circular motion, and the object is accelerated towards the center of the circle. If the radius of the circular path is r, the magnitude of this acceleration is ac = v2 / r, where v is its speed and ac is called the centripetal acceleration. A centripetal force is responsible for the centripetal acceleration, which constantly pulls the object towards the center of the circular path. There cannot be any circular motion without a centripetal force.
Banking
When there is a sharp turn in the road or when a turn has to be taken at a high speed as in a racetrack, the outer part of the road or the track is raised from the inner part of the track. This is called banking. It provides additional centripetal force to a turning vehicle so that it doesn't skid.
The angle of banking is kept just right so that it provides all the centripetal force required and a motorist does not have to depend on the friction force at all.
Inclined Planes
Forces on an Inclined Plane
The inclined plane is a device that reduces the force needed to lift objects. Consider the forces acting on a block on an inclined surface. The inclined surface exerts a normal force FN on the block that is perpendicular to the incline. The force of gravity, FG, points downward. If there is no friction, the net force, Fnet, acting on the block is the resultant of FN and FG. By Newton's second law the net force must point down the incline because the block moves only along the incline and not perpendicular to it.
The vector triangle shows .
After reading this module, you should be able to . . .
10.01 Identify that if all parts of a body rotate around a fixed
axis locked together, the body is a rigid body. (This chapter
is about the motion of such bodies.)
10.02 Identify that the angular position of a rotating rigid body
is the angle that an internal reference line makes with a
fixed, external reference line.
10.03 Apply the relationship between angular displacement
and the initial and final angular positions.
10.04 Apply the relationship between average angular velocity, angular displacement, and the time interval for that displacement.
10.05 Apply the relationship between average angular acceleration, change in angular velocity, and the time interval for
that change.
10.06 Identify that counterclockwise motion is in the positive
direction and clockwise motion is in the negative direction.
10.07 Given angular position as a function of time, calculate the
instantaneous angular velocity at any particular time and the
average angular velocity between any two particular times.
10.08 Given a graph of angular position versus time, determine the instantaneous angular velocity at a particular time
and the average angular velocity between any two particular times.
10.09 Identify instantaneous angular speed as the magnitude
of the instantaneous angular velocity.
10.10 Given angular velocity as a function of time, calculate
the instantaneous angular acceleration at any particular
time and the average angular acceleration between any
two particular times.
10.11 Given a graph of angular velocity versus time, determine the instantaneous angular acceleration at any particular time and the average angular acceleration between
any two particular times.
10.12 Calculate a body’s change in angular velocity by
integrating its angular acceleration function with respect
to time.
10.13 Calculate a body’s change in angular position by integrating its angular velocity function with respect to time.
Rotational dynamics as per class 12 Maharashtra State Board syllabusRutticka Kedare
This ppt is as per class 12 Maharashtra State Board's new syllabus w.e.f. 2020. Images are taken from Google public sources and Maharashtra state board textbook of physics. Gif(videos) from Giphy.com. Only intention behind uploading these ppts is to help state board's class 12 students understand physics concepts.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
4. Contents:
• Rotation
• Angular position and radian
• Angular displacement
• Angular velocity
• Angular acceleration
• Centripetal and centrifugal force
• Torque
• Rotational kinetic energy
• Newton second law of rotation
5. DEFINITION OF ROTATION
• Rotation is when an object turn about
an axis. OR
• A rotation is a circular movement of an
object around a center (or point) of
rotation. A three-dimensional object
can always be rotated around an
infinite number of imaginary lines
called rotation axes. If the axis passes
through the body's center of mass, the
body is said to rotate upon itself, or
spin.
6. ANGULAR POSITION
The orientation of a body or figure with
respect to a specified reference position as
expressed by the amount of rotation necessary to
change from one orientation to the other about a
specified axis.
The angular position, conventionally
denoted by q. This is the angle at a particular
instant in time that the object makes with respect to
some fixed reference axis.
The arc length and r are related:
s= q r
7. ANGULAR DISPLACEMENT:
The angular displacement is defined as
the angle the object rotates through during
some time interval
SI Unit of Angular Displacement: radian (rad)
Where,
This is the angle that the reference line of
length r sweeps out.
f i
q q q
360
1 57.3
2
rad
9. AVERAGE ANGULAR ACCELERATION
The average angular acceleration a, of an object is defined as
the ratio of the change in the angular velocity to the time it takes
for the object to undergo the change.
SI Unit of Angular acceleration: radian per second per second
(rad/s2)
f i
avg
f i
t t t
a
10. EXAMPLE:
A JET REVVING ITS ENGINES
• As seen from the front of the engine, the
fan blades are rotating with an angular
speed of
-110 rad/s. As the plane takes off, the
angular velocity of the blades reaches -330
rad/s in a time of 14s.
• Find the angular acceleration, assuming it
to be constant.
solution: f i
avg
f i
t t t
a
11. Centripetal force :
• CENTRIPETAL FORCE is a force which acts on a body moving in a
circular path and is directed towards the center around which the body
is moving.
OR
Centripetal force is defined as the
radial force directed towards the
center acting on a body in circular
motion.
12. Nature of centripetal force:
• Magnitude of centripetal force
remains constant.
• Always it acts along the radius.
• It is always directed towards the center.
• Hence, centripetal force is a radial force of
constant magnitude.
• The centripetal force –f acting on a body of mass
-m moving in a circular path is given by
f = mv2/r
13. Centripetal Force and Mass:
• Centripetal force is directly
proportional to the mass of the body.
f α m
14. Centripetal Force and Radius:
• Centripetal force is inversely proportional
to the radius of the body.
f α 1/r
15. Centripetal Force and speed:
•Centripetal force is directly proportional
to square of the velocity of the body.
f α v2
16.
17. EXAMPLES OF CENTRIPETAL FORCE:
For a car travelling around a
circular road with uniform speed,
the centripetal force is provided
by the force of static friction
between tyres of the car
and the road.
18. CENTRIFUGAL FORCE
1. Centrifugal force is an imaginary force experienced only in non-inertial
frames of reference.
2. This force is necessary in order to explain Newton’s laws of motion in an
accelerated frame of reference.
3. Centrifugal force is acts along the radius but is directed away from the
center of the circle.
4. Direction of centrifugal force is always opposite to that of the centripetal
force.
5. Centrifugal force f = mv2/r
6. Centrifugal force is always present in rotating bodies.
19. EXAMPLES OF CENTRIFUGAL FORCE:
1. When a car in motion takes a sudden turn towards left, passengers in
the car experience an outward push to the right. This is due to the
centrifugal force acting on the passengers.
2. The children sitting in a merry-go-round experience an outward force
as the merry-go-round rotates about the vertical axis.
20. August 14, 2023
TORQUE:
• Torque, t, is the tendency of a force to
• rotate an object about some axis
• Let F be a force acting on an object, and let r be a position
vector from a rotational center to the point of application of the
force, with F perpendicular to r. The magnitude of the torque is
given by
rF
t
21. August 14, 2023
TORQUE UNITS AND DIRECTION
• The SI units of torque are N.m
• Torque is a vector quantity
• Torque magnitude is given by
• Torque will have direction
• If the turning tendency of the force is counterclockwise, the torque will be
positive
• If the turning tendency is clockwise, the torque will be negative
Fd
rF
q
t sin
22. August 14, 2023
NET TORQUE
• The force will tend to cause a
counterclockwise rotation about O
• The force will tend to cause
clockwise rotation about O
• St t1 + t2 F1d1 – F2d2
• If St 0, starts rotating
• If St 0, rotation rate does not
change
1
F
2
F
Rate of rotation of an object does not change,
unless the object is acted on by a net torque
23. NET FORCE = 0 , NET TORQUE ≠ 0
10 N
10 N
• > The net force = 0, since the forces are applied in
opposite directions so it will not accelerate.
• > However, together these forces will make the rod
rotate in the clockwise direction.
24. NET TORQUE = 0, NET FORCE ≠ 0
The rod will accelerate upward under these
two forces, but will not rotate.
25. ANGULAR MOMENTUM
• The quantity of rotation of a body, which is the product of its
moment of inertia and its angular velocity.
• In physics, angular momentum is the rotational equivalent of
linear momentum.
26. RELATION BETWEEN LINEAR
AND ANGULAR MOMENTUM
• The magnitude of angular momentum l is equal to the
product of the magnitude of vector r and magnitude of vector
p and sine of the angle between r and p.
l = r × p.
29. Rolling Kinetic Energy
Translation Rotation
K.E (total) = K.E (translation) + K.E (rotation)
K.Etotal = ½ mv2 + ½ I 2
Both pieces in units of Joules.
30. NEWTON SECOND LAW OF
ROTATION:
•The rotational form of Newton's second
law states the relation between net
external torque and the angular acceleration of a
body about a fixed axis. The result looks similar to
Newton's second law in linear motion with a few
modifications.
32. NEWTON'S SECOND LAW STATES “That the
angular acceleration is proportional to the net torque
and inversely proportional to the moment of inertia”.
NEWTON'S SECOND LAW:
34. • First consider a case where all the mass
is in one place.
Suppose a point object of
mass ‘m’ attached to a light rigid rod of
length ‘l ’ is rotating about an axis
perpendicular to the rod and passing
through its end. A force acts on the
particle to increase the angular velocity of
rotation. Break the force into its
components. One component is towards
the axis and called the radial component
of force and the other component is in
the tangential direction .
• The torque of the radial component about
the axis is zero as the line of action of the
force is passing through the axis itself.
The torque of the tangential component
will try to increase the object's angular
velocity and produce angular
35. THE NET TORQUE OF THE FORCE ALONG
THE AXIS IS
The acceleration of the particle along the tangential direction will be .
For
motion along a circular path, the object's angular acceleration will be ,
Where R is the radius of the circular path of the particle, which in this case
will be the length of the rod. Thus,
36. Comparing equations (1) and (2),
Now, since the moment of inertia of a particle about the axis of rotation is we
have
t = I α
37. ROTATIONAL FORM OF NEWTON'S SECOND
LAW FOR RIGID BODY
DEFINATION :
If the relative distance between any two particles on
a body remains the same throughout the motion,
then the body is said to be rigid. Such a body
maintains its shape and size irrespective of the
forces acting on it.
38. • If a rigid body is rotating about a fixed
axis and multiple forces are acting on it
to change its angular velocity, then the
body can be to be made up of many
small point masses attached at the end
of mass less rods and rotating about
the same axis. As the body is rigid, all
the particles complete their circular
motion together and the angular
acceleration for all the particles is the
same. Applying the rotational form of
Newton's second law for individual
particles,