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PART II: Back in the day, this is how our parents listened to music- by dropping

ID: 1390712 • Letter: P

Question

PART II: Back in the day, this is how our parents listened to music- by dropping a record on top of a turntable. If the moment of inertia of the turntable is I1 and that of the record is I2, and the turntable is initially rotating with angular frequency w1, find a) the angular velocity of the combined system (record+turntable) after the record lands on the turntable: the final kinetic energy is not the same as the initial (hint: where could the missing b) The kinetic energy of the system if the initial kinetic energy was Kl. Explain why energy go?):

Explanation / Answer

From law of conservation of angular momentum

Angular momentum before attching record = angular momentum after attaching record

amgular momentum = L = I*W

then (I1*w1)+(I2*0) = (I1+I2)*w

let w be the anular velocity of the combined system

w = (I1*w1)/(I1+I2)

B) Rotational KE = (1/2)*I*w^2

initial KE = (1/2)*I1*w1^2

after adding record to the turntable the moment of inertia is increased
hence final KE of the system will changes

Final KE = (1/2)*(I1+I2)*w^2

Final KE = (1/2)*(I1+I2)*(I1*w1)^2/(I1+I2)^2

Final KE = (1/2)*(I1*w1)^2/(I1+I2)

loss in KE = Final KE - initial KE

loss in KE = [(1/2)*(I1*w1)^2/(I1+I2)]-[(1/2)*I1*w1^2]

loss in KE = [(1/2)*I1*w1^2 ][(I1/(I1+I2))-1]
loss in KE = -[(1/2)*I1*I2*w1^2]/(I1+I2)

loss in KE appereas in doing mechanical work done to rotate