A uniform cylindrical turntable of radius 1.50 m and mass 29.2 kg rotates counte

Question

A uniform cylindrical turntable of radius 1.50 m and mass 29.2 kg rotates counterclockwise in a horizontal plane with an initial angular speed of 4? rad/s. The fixed turntable bearing is frictionless. A lump of clay of mass 2.49 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.40 m to the east of the axis. (a) Find the final angular speed of the clay and turntable. (b) Is mechanical energy of the turntable-clay system constant in this process? (yes or no) What, if any, is the change in internal energy? (c) Is momentum of the system constant in this process? (Yes or no) What, if any, is the amount of impulse imparted by the bearing? (magnitude and direction)

Explanation / Answer

(a)

Initial angular momentum :

I(initial) = 0.5*M*R^2*wi

=0.5*29.2*1.5^2*4 = 412.805

Final angular momentum:

I(final) = (0.5*29.2*1.5^2+2.49*1.4^2)*w = 37.7304*w

Momentum will remain conserved;

37.7304*w =  412.805

w = 10.941 rad/s

(b)

Original KE= 0.5 . I . w^2

=0.5*0.5*29.2*1.5^2*(4)^2= 2593.732 J

Fianl KE= 0.5 . I . w^2

=0.5*37.7304*(10.941 )^2= 2258.268 J

So mechanical energy is not constant in the process.

The change in internal energy = 2593.732- 2258.268 = 335.464 J

(c)

Angular momentum is conserved.

The system is isolated by the frictionless bearings

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