Question

A uniform cylindrical turntable of radius 2.00 m and mass 31.2 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 2.42 kg and negligible size is dropped onto the turntable from a small distance above it and immediately sticks to the turntable at a point 1.90 m to the east of the axis.

1. Find the final angular speed of the clay and turntable.

a. magnitude _____ in	rad/s
b. direction	(clockwise or counterclockwise)

2.

a. Is mechanical energy of the turntable-clay system constant in this process?

Yes or No    

b. What is the change in internal energy?
_________J

3. Is momentum of the system constant in this process?

Yes or No    

4. What, if any, is the amount of impulse imparted by the bearing?

a. magnitude	________ kg · m/s
b. direction (north or south)

Answer 1

1)

Conserving the angular momentum of the system:

I1*W1 = (I1 + I2)*W

So, (0.5*31.2*2^2)*(4*pi) = (0.5*31.2*2^2 + 2.42*1.9^2)*W

So, W = 11.02 rad/s <-------- answer

direction = counterclockwise <------ answer

2)

a)

Mechanical energy of the system is not constant as the colision is not perfectly elastic

b)

change in internal energy = 0.5*(I1)*W1^2 - 0.5*(I1 + I2)*W^2

= 0.5*(31.2*2^2*(4*pi)^2 - (31.2*2^2 + 2.42*1.9^2)*(11.02)^2)

= 1745.5 J <------ answer

3)

Yes, momentum of the system is constant as there are no other forces acting on the system

4)

Impulse imparted by the bearing :

a) impulse = m*v = 2.42*(11.02*1.9)

= 50.7 kg.m/s

b) direction = north