Question

A 230 g , 44.0-cm-diameter turntable rotates on frictionless bearings at 59.0 rpm . A 24.0 g block sits at the center of the turntable. A compressed spring shoots the block radically outward along a frictionless groove in the surface of the turntable.

Part A What is the turntable's rotation angular velocity when the block reaches the outer edge? Express your answer with the appropriate units.

Answer 1

here,

mass of turntable , m1 = 230 g = 0.23 kg

diameter , d = 44 cm = 0.44 m

radius , r = d/2 = 0.22 m

the mass of block , m2 = 24 g = 0.024 kg

initial angular velocity , w0 = 59 rpm

let the final angular velocity be w

using conservation of angular momentum

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

(0.5 * 0.23 ) * 59 = (0.5 * 0.23 + 0.024) * w

solving for w

w = 48.8 rev/s

the new angular velocity is 48.8 rev/s