In: Physics
A 1.8 kg , 20-cm-diameter turntable rotates at 130 rpm on frictionless bearings. Two 510 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick.What is the turntable's angular velocity, in rpm, just after this event?
Mass of the turntable = M = 1.8 kg
Diameter of the turntable = D = 20 cm = 0.2 m
Radius of the turntable = R = D/2 = 0.2/2 = 0.1 m
Moment of inertia of the turntable = I
I = MR2/2
I = (1.8)(0.1)2/2
I = 9 x 10-3 kg.m2
Initial angular speed of the turntable = 1 = 130 rpm
Converting the angular speed to rad/s,
1 = 13.614 rad/s
Mass of each block = m = 510 g = 0.51 kg
Number of blocks = n = 2
The blocks hit the turntable at opposite ends of a diameter therefore each block is at a distance equal to the radius from the rotation axis.
Final angular speed of the turntable = 2
By conservation of angular momentum,
I1 = (I + mR2 + mR2)2
(9x10-3)(13.614) = [9x10-3 + (0.51)(0.1)2 + (0.51)(0.1)2]2
2 = 6.381 rad/s
Converting the angular speed to rpm,
2 = 60.93 rpm
Angular velocity of the turntable after the event = 60.93 rpm