Question

A 1.5 kg , 20-cm-diameter turntable rotates at 50 rpm on frictionless bearings. Two 470 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. Part A What is the turntable's angular velocity, in rpm, just after this event? Express your answer to two significant figures and include the appropriate units. w=?

Answer 1

Mass of the turn table = M = 1.5 kg

Diameter of the turn table = D = 20 cm = 0.2 m

Radius of the turn table = R = D/2 = 0.2/2 = 0.1 m

Moment of inertia of the turn table = I

I = 0.0075 kg.m²

Initial angular speed of the turn table = ₁ = 50 rpm = 50 x (2/60) rad/s = 5.236 rad/s

Number of blocks = n

Mass of each block = m = 470 g = 0.47 kg

The blocks fall on the opposite ends of a diameter therefore the blocks are at a distance equal to the radius of the turn table from the center.

Angular speed of the turn table after the blocks fall on it = ₂

By conservation of angular momentum,

₂ = 2.324 rad/s

Converting from rad/s to rpm,

₂ = 22.2 rpm

A) Angular velocity of the turn table after the blocks fall on it = 22.2 rpm