Question

A carousel has a radius of 1.60 m and a moment of inertia of 110 kg · m2 . A girl of mass 42.5 kg is standing at the edge of the carousel, which is rotating with an angular speed of 3.20 rad/s. Now the girl walks toward the center of the carousel and stops at a certain distance from the center d. The angular speed of the carousel is now 5.2 rad/s. How far from the center did the girl stop?

Answer 1

here,

the radius of the carousel ,r = 1.6 m

moment of inertia , I = 110 kg.m^2

mass of girl , m = 42.5 kg

initial angular speed , w0 = 3.2 rad/s

final angular speed , w = 5.2 rad/s

let the distance from center where the girl stops be x

using conservation of angular momentum

(I + m * r^2) * w0 = (I + m * x^2) * w

( 110 + 42.5 * 1.6^2) * 3.2 = ( 110 + 42.5 * x^2) * 5.2

solving for x

x = 0.76 m

the final distance of girl from the center is 0.76 m