A merry-go-round modeled as a disk of mass M = 1.00x10^2 kg and radius R = 2.00

Question

A merry-go-round modeled as a disk of mass M = 1.00x10^2 kg and radius R = 2.00 m is rotating in a horizontal plane about a frictionless vertical axle (see figure). (a) After a student with mass m = 60.0 kg jumps on the rim of the merry-go-round, the system's angular speed decreases to 2.00 rad/s. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.500 m from the center. (b) Find the change in the system's rotational kinetic energy caused by her movement to the center. (c) Find the work done on the student as she walks to r = 0.500 m.

Explanation / Answer

I=mr^2+1/2MR^2 to I=m(r2)^2+1/2MR^2 I1*W1=I2*W2 W2=I1/I2*W1 W2=(mr^2+1/2MR^2)/(m(r2)^2+1/2MR^2)*W1 W2=(60*2^2+1/2*100*2^2)/(60*.5^2+1/2*100*2^2)*2 =4.09 r/s W=Change in KE W=1/2*I2W2^2-1/2*I1W1^2 W=1/2*(60*.5^2+1/2*100*2^2)*4.09^2-1/2*(60*2^2+1/2*100*2^2)*2^2 =918.27

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