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)|
a. Is mechanical energy of the turntable-clay system constant in this process?
Yes or No
b. What is the change in internal energy?
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)|
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
Mechanical energy of the system is not constant as the colision is not perfectly elastic
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
Yes, momentum of the system is constant as there are no other forces acting on the system
Impulse imparted by the bearing :
a) impulse = m*v = 2.42*(11.02*1.9)
= 50.7 kg.m/s
b) direction = north
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