A 6.81 kg turntable is free to rotate on its axis. The turntable has a radius of

Question

A 6.81 kg turntable is free to rotate on its axis. The turntable has a radius of 0.470 m and is rotating at a rate of 75.0 rad/s.

a) What is the rotational inertia of the turntable? (assume it is a uniform disk)

b)What is the angular momentum of the turntable?

c) A 2.50 kg piece of clay falls directly down on to the turntable at a position 0.360 m from the center and sticks.  What is the moment of inertia of the combination (disk and mass)?

d)What is the final angular velocity?

e)What is the change in kinetic energy?

Explanation / Answer

A 6.81 kg turntable is free to rotate on its axis. The turntable has a radius of 0.470 m and is rotating at a rate of 75.0 rad/s.

a)     What is the rotational inertia of the turntable? (assume it is a uniform disk)

b)    What is the angular momentum of the turntable?

c)     A 2.50 kg piece of clay falls directly down on to the turntable at a position 0.360 m from the center and sticks. What is the moment of inertia of the combination (disk and mass)?

d)    What is the final angular velocity?

e)     What is the change in kinetic energy?

ans :

a ,

I = 0.5 * 6.81 * 0.47^2 = 0.75

b.

L = 0.75 * 75 = 56.4

c.

I =[ 0.75 + 2.5 * 0.36^2] = 1.07

d.

0.75 * 75 = 1.07 w

w = 52.3 ra d / s

e.

K2 - K1 = 0.5 [ 1.07* 52.3^2 - 0.75* 75^2 ]

= 640 J

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