Physics: Principles with Applications
Physics: Principles with Applications
6th Edition
ISBN: 9780130606204
Author: Douglas C. Giancoli
Publisher: Prentice Hall
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Question
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Chapter 8, Problem 61P

(a)

To determine

The angular velocity.

(a)

Expert Solution
Check Mark

Answer to Problem 61P

The angular velocity of the platform when person reaches the edge is 1.32rad/s

Explanation of Solution

Given:

Moment of inertia of merry-go-round, I1=920kgm2

Mass of person, M=75kg

Radius of merry-go-round, R=3.0m

Initial angular velocity of platform, ω1=2rad/s

Formula used:

Moment of inertia of person, I=MR2

Law of conservation of angular momentum, I1ω1=(I1+I2)ω'

Calculation:

Substituting values for moment of inertia of person,

   I 2 =(75) (3) 2 I2=675kgm2

Substituting values in law of conservation of angular momentum,

  (920)(2)=(920+675)ω'ω'=18401395ω'=1.32rad/s

Conclusion:

The angular velocity of the platform when person reaches the edge is 1.32rad/s

(b)

To determine

The rotational kinetic energy of the system.

(b)

Expert Solution
Check Mark

Answer to Problem 61P

The rotational kinetic energy of the platform before the person walks is 1840J

The rotational kinetic energy of the platform after the person walks is 1390J

Explanation of Solution

Given:

Moment of inertia of merry-go-round, I1=920kgm2

Moment of inertia of person, I2=675kgm2

Initial angular velocity of platform, ω1=2rad/s

Final angular velocity of platform, ω'=1.32rad/s

Formula used:

Rotational kinetic energy is given by, K=12Iω2

Calculation:

Substituting values for rotational kinetic energy before man walks,

  K1=12I1ω12 K 1 = 1 2 (920) (2) 2 K1=1840J

Substituting values for rotational kinetic energy after man walks,

   K 2 = 1 2 ( I 1 + I 2 ) (ω') 2 K 2 = 1 2 (920+675) (1.32) 2 K2=1390J

Conclusion:

The rotational kinetic energy of the platform before the person walks is 1840J

The rotational kinetic energy of the platform after the person walks is 1390J

Chapter 8 Solutions

Physics: Principles with Applications

Ch. 8 - The moment of inertia of a rotating solid disk...Ch. 8 - Two inclines have the same height but make...Ch. 8 - Two spheres look identical and have the same mass....Ch. 8 - A sphere and a cylinder have the same radius and...Ch. 8 - Prob. 15QCh. 8 - Prob. 16QCh. 8 - Prob. 17QCh. 8 - 15. Can the diver of Fig. 8-28 do a somersault...Ch. 8 - Prob. 19QCh. 8 - When a motorcyclist leaves the ground on a jump...Ch. 8 - Prob. 21QCh. 8 - 18. The angular velocity of a wheel rotating on a...Ch. 8 - 19. In what direction is the Earth's angular...Ch. 8 - 20. ‘On the basis of the law of conservation of...Ch. 8 - Prob. 1PCh. 8 - Prob. 2PCh. 8 - Prob. 3PCh. 8 - Prob. 4PCh. 8 - Prob. 5PCh. 8 - Prob. 6PCh. 8 - Prob. 7PCh. 8 - Prob. 8PCh. 8 - Prob. 9PCh. 8 - Prob. 10PCh. 8 - Prob. 11PCh. 8 - Prob. 12PCh. 8 - Prob. 13PCh. 8 - Prob. 14PCh. 8 - Prob. 15PCh. 8 - Prob. 16PCh. 8 - Prob. 17PCh. 8 - Prob. 18PCh. 8 - Prob. 19PCh. 8 - Prob. 20PCh. 8 - Prob. 21PCh. 8 - Prob. 22PCh. 8 - Prob. 23PCh. 8 - Prob. 24PCh. 8 - Prob. 25PCh. 8 - Prob. 26PCh. 8 - Prob. 27PCh. 8 - Prob. 28PCh. 8 - Prob. 29PCh. 8 - Prob. 30PCh. 8 - Prob. 31PCh. 8 - Prob. 32PCh. 8 - Prob. 33PCh. 8 - Prob. 34PCh. 8 - Prob. 35PCh. 8 - Prob. 36PCh. 8 - Prob. 37PCh. 8 - Prob. 38PCh. 8 - Prob. 39PCh. 8 - Prob. 40PCh. 8 - Prob. 41PCh. 8 - Prob. 42PCh. 8 - Prob. 43PCh. 8 - Prob. 44PCh. 8 - Prob. 45PCh. 8 - Prob. 46PCh. 8 - Prob. 47PCh. 8 - Prob. 48PCh. 8 - Prob. 49PCh. 8 - Prob. 50PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Prob. 53PCh. 8 - Prob. 54PCh. 8 - Prob. 55PCh. 8 - Prob. 56PCh. 8 - Prob. 57PCh. 8 - Prob. 58PCh. 8 - Prob. 59PCh. 8 - Prob. 60PCh. 8 - Prob. 61PCh. 8 - Prob. 62PCh. 8 - Prob. 63PCh. 8 - Prob. 64PCh. 8 - Prob. 65PCh. 8 - Prob. 66PCh. 8 - Prob. 67PCh. 8 - Prob. 68GPCh. 8 - Prob. 69GPCh. 8 - Prob. 70GPCh. 8 - Prob. 71GPCh. 8 - Prob. 72GPCh. 8 - Prob. 73GPCh. 8 - Prob. 74GPCh. 8 - Prob. 75GPCh. 8 - Prob. 76GPCh. 8 - Prob. 77GPCh. 8 - Prob. 78GPCh. 8 - Prob. 79GPCh. 8 - Prob. 80GPCh. 8 - Prob. 81GPCh. 8 - Prob. 82GPCh. 8 - Prob. 83GPCh. 8 - Prob. 84GPCh. 8 - Prob. 85GPCh. 8 - Prob. 86GP
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