Question

A 1.9 kg , 20-cm-diameter turntable rotates at 150 rpm on frictionless bearings. Two 520 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is the turntable's angular velocity, inrpm, just after this event?

Answer 1

Answer: 73.08 rpm

Explanation:

Given

Mass of the table, m(t) = 1.9 kg

Radius of table, r = 20/2 cm = 10 cm = 0.1 m

Mass of the block, m(b) = 500 g = 0.5 kg

Speed of rotation, w(i) = 150 rpm

Using conservation of angular momentum, where, initial angular momentum is equal to final angular momentum

L(i) = L(f)

I(i)w(i) = I(f)w(f)

w(f) = I(i)w(i) / I(f)

also, moment of inertia a disk or cylinder is I = 1/2mr²

Thus, I(i) = 1/2 mr²

I(i) = 1/2 * 1.9 * 0.1²

I(i) = 0.0095 kgm²

I(f) = Σm(i)r(i)² = I(i) + I(block1) + I(block2)

I(f) = I(i) + I(a) + I(b)

I(f) = 0.0095 + m(a)r(a)² + m(b)r(b)²

Remember, r(a) = r(b) = R

m(a) = m(b) = M, so that

I(f) = 0.0095 + MR² + MR²

I(f) = 0.0095 + 2MR²

I(f) = 0.0095 + 2 * 0.5 * 0.1²

I(f) = 0.0095 + 0.01

I(f) = 0.0195 kgm²

Substituting for values in the first equation

w(f) = I(i)w(i) / I(f)

w(f) = (0.0095 * 150) / 0.0195

w(f) = 1.425 / 0.0195

w(f) = 73.08 rpm

Thus, the turntable's angular velocity is 73.08 rpm