A uniform cylindrical turntable of radius 1.70 m and mass 32.7 kg rotates counte

Question

A uniform cylindrical turntable of radius 1.70 m and mass 32.7 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4pi rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass 2.45 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.60 m to the east of the axis. Find the final angular speed of the clay and turntable. Is mechanical energy of the turntable-clay system constant in this process? Yes No What, if any, is the change in internal energy? Is momentum of the system constant in this process? Yes No What, if any, is the amount of impulse imparted by the bearing?

Explanation / Answer

a) Using angular momentum (Iw) conservation,

initial angular momentum = final momentum

(32.7 x 1.70^2 /2 ) (4pi ) + 0 = (32.7 x 1.70^2 / 2)(wf) + (2.45 x 1.60^2)wf

wf = 3.53pi rad/s

direction will be same as initial direction.

direction -> counterclockwise

b) No, energy will not be conserved.

initial energy = Iw^2 /2 = (32.7 x 1.70^2 / 2) ( 4pi)^2 /2 + 0

= 3730.83 J

final energy = (32.7 x 1.70^2 / 2) ( 3.53 pi)^2 /2 + (2.45 x 1.60^2)(3.53 pi)^2 /2

= 3291.27 J

change in energy = - 439.56 J

c) Yes momentum will be conserved.

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