Question

A 26 g block sits at the center of a turntable that rotates at 70 rpm. A compressed spring shoots the block radially outward from the center along a frictionless groove in the surface of the turntable. Calculate the turntable's angular speed when the block reaches the outer edge. Treat the turntable as a solid disk with mass with mass 200 g and diameter 50.0 cm. Express your answer in revolutions per minute.

Answer 1

here,

mass of turntable , m1 = 200 g = 0.2 kg

diameter , d = 50 cm = 0.5 m

radius , r = d/2 = 0.25 m

mass of block ,m2 = 26 g = 0.026 kg

initial angular speed , w0 = 70 rpm

let the final angular speed be w

using conservation of angular momentun

(0.5 * m1 * r^2) * w0 = ( 0.5 * m1 * r1^2 + m2 * r1^2) * w

(0.5 * 0.2 ) * 70 = ( 0.5 * 0.2 + 0.026) * w

solving for w

w = 55.56 rpm

the final angular speed is 55.56 rpm