Question

A playground merry-go-round has a mass of 120 kg and a radius of 1.80 m and it is rotating with an angular velocity of 0.500 rev/s. What is its angular velocity after a 22.0-kg child gets onto it by grabbing its outer edge? The child is initially at rest.

a) 0.320 rev/s
b) 0.375 rev/s
c) 0.450 rev/s
d) 0.550 rev/s

Answer 1

The angular velocity of the merry-go-round after a child gets on can be calculated using the law of conservation of angular momentum. By adding the mass of the child to the moment of inertia, we can find the new angular velocity.

Step-by-step explanation:

The angular momentum of the merry-go-round before the child gets on can be calculated using the formula:

Angular Momentum = moment of inertia * angular velocity

Plugging in the given values, we have:

Angular Momentum = (120 kg * 1.80 m^2) * (0.500 rev/s) = 108 kg*m^2/s

When the child gets onto the merry-go-round, the moment of inertia increases since the child adds to the total mass. The new angular momentum can be calculated using the formula:

New Angular Momentum = (moment of inertia before + mass of child * radius^2) * new angular velocity

Plugging in the known values, we get:

New Angular Momentum = ((120 kg * 1.80^2 m^2) + (22 kg * 1.80 m)^2) * angular velocity after

We can solve for the new angular velocity:

new angular velocity = New Angular Momentum / ((120 kg * 1.80^2 m^2) + (22 kg * 1.80 m)^2) = 0.375 rev/s

Therefore, the answer is b) 0.375 rev/s.