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Back in the day, this is how our parents listened to music - by dropping a recor

ID: 1388675 • Letter: B

Question

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 intertia 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:

b) The kinetic energy of the system if the initial kinetic energy was K1. Explain why the final kinetic energy is not the same as the initial (hint: where could the missing energy go?):

Explanation / Answer

Here ,

a)

Using conservation of angular momentum

w2 * (I1 + I2 ) = w1 * I1

w2 = w1*I1/(I1 + I2)

the angular velocity of combined system is w1*I1/(I1 + I2)

b)

Here ,

final kinetic energy = 0.5 * (I1 + I2) * w2^2

K2 = 0.5 * (I1 + I2)*( w1*I1/(I1 + I2))^2

K2 = 0.5 * I1 * w1^2 /(I1 + I2)

K2 = K1/(I1 + I2)

the final kinetic energy is K1/(I1 + I2)

the missing energy dissipated as heat generated when the contact is made