Book cover for Physics

Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

ISBN #9781118486894

10th Edition

2,562 Questions

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Homework Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

Rotational dynamics mirrors many concepts from linear motion, with torque acting as the rotational counterpart to force and moment of inertia serving as a measure of resistance to angular acceleration. For rigid bodies, equilibrium requires both the net force and net torque to vanish. Conservation principles, such as those for angular momentum, explain a wide range of phenomena from spinning skaters to orbiting satellites. Translational and rotational work and energy can be analyzed in parallel, with applications spanning engineering, biomechanics, and everyday devices like cranes, ladders, and springs.

Learning Objectives

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Key Concepts

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DEFINITION

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Example Problems

Example 1

The wheel of a car has a radius of 0.350 m. The engine of the car applies a torque of 295 N ? m to this wheel, which does not slip against the road surface. Since the wheel does not slip, the road must be applying a force of static friction to the wheel that produces a counter- torque. Moreover, the car has a constant velocity, so this counter torque balances the applied torque. What is the magnitude of the static frictional force?

Example 2

The steering wheel of a car has a radius of 0.19 m, and the steering wheel of a truck has a radius of 0.25 m. The same force is applied in the same direction to each steering wheel. What is the ratio of the torque produced by this force in the truck to the torque produced in the car?

Example 3

You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 4$$5 \mathrm{N} \cdot \mathrm{m}$$. Using the data in the drawing, determine the magnitude F of the force that you must exert on the wrench.

Example 4

Two children hang by their hands from the same tree branch. The branch is straight, and grows out from the tree trunk at an angle of 27.08 above the horizontal. One child, with a mass of 44.0 kg, is hanging 1.30 m along the branch from the tree trunk. The other child, with a mass of 35.0 kg, is hanging 2.10 m from the tree trunk. What is the magnitude of the net torque exerted on the branch by the children? Assume that the axis is located where the branch joins the tree trunk and is perpendicular to the plane formed by the branch and the trunk.

Example 5

The drawing shows a jet engine suspended beneath the wing of an airplane. The weight $\mathrm{W}$ of the engine is $10200 \mathrm{N}$ and acts as shown in the drawing. In flight the engine produces a thrust T of 62300 N that is parallel to the ground. The rotational axis in the drawing is perpendicular to the plane of the paper. With respect to this axis, find the magnitude of the torque due to (a) the weight and (b) the thrust.
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Step-by-Step Explanations

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Common Mistakes

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