Joey, whose mass is m = 36 kg, stands at rest at the outer edge of a frictionless merry-go-round with the mass M = 300 kg and the radius R = 2.0 m. The merry-go-round is also at rest. Joey then begins to run around the perimeter of the merry-go-round, finally reaching a constant speed, measured relative to the ground, of 4.0 m/s. What is the final angular speed of the merry-go-round?

Explanation:

Given:

mass of person,

mass of merry go-round,

radius of merry go-round,

velocity of the person running,

We consider merry go-round as a ring:

Now the moment of inertial of the ring is given as,

Moment of inertia of the person considering as a point mass:

Now according to the conservation of angular momentum:

where:

angular velocity of the merry-go-round

angular velocity of the person running