Assignmentopmet | 20116 Chapter 11, Problem 052 Your answer is partially correct

Question

Assignmentopmet | 20116 Chapter 11, Problem 052 Your answer is partially correct. Try again. A cockroach of mass m lies on the rim of a uniform disk of mass 8.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.457 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? Review Seore oblective(b) What is the ratio K/Ko of the new kinetic energy of the system to its initial kinetic energy? Mobie Site (a) = (b) K/Ko = Question Attempts: 2of‘used sav, ro. LATE.

Explanation / Answer

initial angular momentum Li = (Idisk + I1)*w1

I1 = initial moment of inertia of inertia = m*R^2

Idisk = (1/2)*M*R^2

M = 8m

final angular momentum Lf = (Idisk + I2)*w2

I2 = final moment of inertia of inertia = m*(R/2)^2

from momentum conservation

Lf = Li

(Idisk + I2)*w2 = (Idisk + I1)*w1

((1/2)*8m*R^2 + m*R^2/4)*w2 = ((1/2)*8m*R^2 + m*R^2)*0.457

(4 + 1/4 )*w2 = (1/2 + 1)*0.457

angular velocity w2 = 0.538 rad/s

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(b)

K = (1/2)*(Idisk + mR^2/4)*w2^2

Ko = (1/2)*(Idisk + mR^2)*w1^2

K/Ko = (4 + 1/4)*0.538^2 / ((4 + 1)*0.457^2)

K/Ko = 1.18 <<<<<=======ANSWER

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