Question

The children have masses of 22.4, 29.0, and 38 kg. If the child who has a mass of 29.0 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm

Answer 1

mass of merry goround = 142 Kg

radius=1.60 m

RPM = 19.3

M1 = 22.4Kg ; M2 = 29.0 Kg ; M3 =38.8 Kg

M2 moves to centre , RPM ' = ?

I = 142 Kg*(1.60m)^2+22.4Kg*(1.60m)^2 +29.0Kg*(1.60m)^2+38.8Kg*(1.60m)^2 =594.4 Kg-m^2

I' = 142 Kg*(1.60m)^2+22.4Kg*(1.60m)^2 +38.8Kg*(1.60m)^2    = 520.2 Kg-m^2

Conservation of Angular momentum requires that

$I*\omega = I'*\omega'$

since angular velocity is directly proportional to RPM

594.4 Kg-m^2* 19.3 = 520.2*RPM'

RPM' = 594.4*19.3/520.2 = 22.1 RPM