Book cover for Physics

Physics

Alan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

ISBN #9780073404530

2nd Edition

2,795 Questions

Group icon
250,136 Students Helped

Homework Questions

Right arrow
Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the fundamentals of rotational dynamics including torque, rotational inertia, and angular momentum. We learn how forces cause rotational motion and how energy is partitioned between translational and rotational motions in rolling objects. Conservation laws, particularly that of angular momentum, are central to understanding phenomena ranging from figure skating and machinery operation to planetary orbits. An essential idea is that even small changes in mass distribution result in significant changes in angular speed, as exemplified by the skater and the mouse-on-a-wheel problems.

Learning Objectives

1

-

2

2.

3

D

4

e

5

s

Key Concepts

CONCEPT

DEFINITION

No concepts available

No definitions available for this book.

Example Problems

Example 1

Verify that $\frac{1}{2} I \omega^{2}$ has dimensions of energy.

Example 2

What is the rotational inertia of a solid iron disk of mass $49 \mathrm{kg},$ with a thickness of $5.00 \mathrm{cm}$ and radius of $20.0 \mathrm{cm}$ about an axis through its center and perpendicular to it?

Example 3

A bowling ball made for a child has half the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume). By what factor is the (a) mass and (b) rotational inertia of the child's ball reduced compared with the adult ball?

Example 4

Find the rotational inertia of thesystem of point particles shown in the figure assuming the system rotates about the (a) $x$ -axis, (b) $y$ -axis, (c) z-axis. The $z$ -axis is perpendicular to the $x y$ -plane and points out of the page. Point particle $A$ has a mass of $200 \mathrm{g}$ and is located at $(x, y, z)=(-3.0 \mathrm{cm}, 5.0 \mathrm{cm}, 0)$ point particle $B$ has a mass of $300 \mathrm{g}$ and is at $(6.0 \mathrm{cm}, 0$ 0), and point particle $C$ has a mass of $500 \mathrm{g}$ and is at $(-5.0 \mathrm{cm},-4.0 \mathrm{cm}, 0) .$ (d) What are the $x$ - and $y$ -coordinates of the center of mass of the system? (FIGURE CAN'T COPY)

Example 5

Four point masses of $3.0 \mathrm{kg}$ each are arranged in a square on massless rods. The length of a side of the square is $0.50 \mathrm{m} .$ What is the rotational inertia for rotation about an axis (a) passing through masses $B$ and $C ?$ (b) passing through masses $A$ and $C ?$ (c) passing through the center of the square and perpendicular to the plane of the square? (FIGURE CAN'T COPY)
Scroll left
Scroll right

Step-by-Step Explanations

Scroll left
Scroll right

Common Mistakes

  • -
  • 2.
  • C
  • o
  • n