Question

A playground merry-go-round of radius 2.5 m
has a moment of inertia 204 kg.m2 and is
rotating at 13 rev/min about a frictionless
vertical axle. Facing the axle, a 21 kg child
hops onto the merry-go-round, and manages
to sit down on the edge.
What is the new angular speed of the
merry-go-round?
Answer in units of rev/min

Answer 1

You need to use conservation of angular momentum by calculating the new moment of inertia once the kid hops on - you can treat her as a point mass at radius r

\[ L_i = L_f\]
\[I_{i}\omega_i=I_f\omega_f\]
\[ \quad \quad I_f=I_i + m_cr^2\]
\[m_c = \text{mass of child}
\\ r = \text{ radius of merry go round}\]