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A cord is wrapped around the rim of a solid uniform wheel

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 12E Chapter 10

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 12E

A cord is wrapped around the rim of a solid uniform wheel 0.250 m in radius and of mass 9.20 kg. A steady horizontal pull of 40.0 N to the right is exerted on the cord, pulling it off tangentially from the wheel. The wheel is mounted on frictionless bearings on a horizontal axle through its center. (a) Compute the angular acceleration of the wheel and the acceleration of the part of the cord that has already been pulled off the wheel. (b) Find the magnitude and direction of the force that the axle exerts on the wheel. (c) Which of the answers in parts (a) and (b) would change if the pull were upward instead of horizontal?

Step-by-Step Solution:

Solution 12E Step 1: Torque = F R Where, F - Force applied, R - radius of the sphere Or, torque = I Where, I - Moment of inertia, - angular acceleration So, F R = I 2 Provided, F = 40 N, R = 0.250 m, I = ½ MR (for solid uniform wheel) Where, M - mass of the wheel and R - radius of the wheel I = ½ × 9.20 kg × (0.250 m) = 4.60 kg × 0.0625 m = 0.2875 kg m 2 2 40 N × 0.250 m = 0.0029 kg m × Rearranging, = (40 N × 0.250 m) / 0.2875 kg m = 34.78 rad/s 2 Angular acceleration of the disc, = 34.78 rad/s 2

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Chapter 10, Problem 12E is Solved
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Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

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A cord is wrapped around the rim of a solid uniform wheel