This chapter discusses rotational motion and related concepts like angular quantities, torque, rotational inertia, and rotational kinetic energy. It defines angular variables like angular velocity and acceleration and relates them to linear motion. It also covers rotational dynamics, determining moments of inertia, and why a rolling object will slow down due to deformation at the point of contact.
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.
Part II:
When r= 0.7r
Part II:
When r= 0
Reflection on this week’s Objectives
Discuss this week’s objectives:
Objectives / Competencies:
· Analyze internal organizational dynamics and the influence on business continuity.
· Describe cultural, structural, leadership considerations that must be incorporated into strategy implementation.
· Determine the resources needed for strategy implementation
Prepare a 350- to 1,050- word paper detailing the findings of your discussion.
Part ! :
Part II :
When r = ro
Part II:
When r= .8ro
Physics161
Moment of Inertia
Introduction
In this experiment we will study the effect of a constant torque on a symmetrical body. In Part I you will determine the angular acceleration of a disk when a constant torque is applied to the disk. From this we will measure its moment of inertia, which we will compare with a theoretical value. In Part II, you will observe the relationship between torque, moment of inertia and angular acceleration for a rotating rod with two masses on either end. You will vary the mass connected (and therefore the torque applied) to the rod by two pulleys. You will also change the moment of inertia of the rod system by changing the distance of the masses from the center of mass of the rod. Reference
Young and Freedman, University Physics, 13th Edition: Chapter 3, section 4; Chapter 9, sections
1-4Theory
Moment of inertia is a measure of the distribution of mass in a body and how difficult that body is to accelerate angularly. For both parts of the experiment, a falling mass will accelerate a rotating object in the horizontal plane. In Part I, the object will be a disk. In Part II, you will find the moment of inertia of a rod with two masses attached to it.
The basic equation for rotational motion is:
(1)
where is angular acceleration in units of rad/s2, is applied torque in N m, and finally I is the moment of inertia or rotational inertia in units of kg m2. For a uniform disk pivoted about the center of mass, the theoretical moment of inertia is
(2)
where M is the mass of the disk and R is the radius of the disk. In Part I we measure the angular acceleration, α, and use this to calculate moment of inertia, I, which we will compare with the theoretical value of I.
In Part II the moment of inertia is the sum of the moments of inertia of the two masses and the rod. For the masses that slip onto the rod, we will assume point masses. Thus, the moment of inertia for one of the two masses is:
(3)
where r is the distance of the center of mass from the axis of rotation located at the center of the rod. Because the masses can be moved along the rod, r will be adjusted to change their moment of inertia. The moment of the inertia of the rod with mass M and a length L is:
(4)
The moment of inertia for a rod with length L and two masses on each end at a distance r is simply the sum of the.
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.
More Related Content
Similar to Chap1d_Lecture_Ch10 Rotational motion (2).ppt
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.
Part II:
When r= 0.7r
Part II:
When r= 0
Reflection on this week’s Objectives
Discuss this week’s objectives:
Objectives / Competencies:
· Analyze internal organizational dynamics and the influence on business continuity.
· Describe cultural, structural, leadership considerations that must be incorporated into strategy implementation.
· Determine the resources needed for strategy implementation
Prepare a 350- to 1,050- word paper detailing the findings of your discussion.
Part ! :
Part II :
When r = ro
Part II:
When r= .8ro
Physics161
Moment of Inertia
Introduction
In this experiment we will study the effect of a constant torque on a symmetrical body. In Part I you will determine the angular acceleration of a disk when a constant torque is applied to the disk. From this we will measure its moment of inertia, which we will compare with a theoretical value. In Part II, you will observe the relationship between torque, moment of inertia and angular acceleration for a rotating rod with two masses on either end. You will vary the mass connected (and therefore the torque applied) to the rod by two pulleys. You will also change the moment of inertia of the rod system by changing the distance of the masses from the center of mass of the rod. Reference
Young and Freedman, University Physics, 13th Edition: Chapter 3, section 4; Chapter 9, sections
1-4Theory
Moment of inertia is a measure of the distribution of mass in a body and how difficult that body is to accelerate angularly. For both parts of the experiment, a falling mass will accelerate a rotating object in the horizontal plane. In Part I, the object will be a disk. In Part II, you will find the moment of inertia of a rod with two masses attached to it.
The basic equation for rotational motion is:
(1)
where is angular acceleration in units of rad/s2, is applied torque in N m, and finally I is the moment of inertia or rotational inertia in units of kg m2. For a uniform disk pivoted about the center of mass, the theoretical moment of inertia is
(2)
where M is the mass of the disk and R is the radius of the disk. In Part I we measure the angular acceleration, α, and use this to calculate moment of inertia, I, which we will compare with the theoretical value of I.
In Part II the moment of inertia is the sum of the moments of inertia of the two masses and the rod. For the masses that slip onto the rod, we will assume point masses. Thus, the moment of inertia for one of the two masses is:
(3)
where r is the distance of the center of mass from the axis of rotation located at the center of the rod. Because the masses can be moved along the rod, r will be adjusted to change their moment of inertia. The moment of the inertia of the rod with mass M and a length L is:
(4)
The moment of inertia for a rod with length L and two masses on each end at a distance r is simply the sum of the.
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.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
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.
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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.