A 3.7 m diameter merry-go-round is rotating freely with an angular velocity of 0.63 rad/s. Its total moment of inertia is 1600 kg\cdot m^2. Four people standing on the ground, each of mass 70 kg, suddenly step onto the edge of the merry-go-round.

Answer 1

You have not said what the question is. Presumably, they want to know the angular velocity after the four people step on.

You can solve for that by using the fact that total angular momentum is conserved. Let the initial and final angular velocity be w1 and w2, respectively.

I*w1 = (I + 4*M*R^2)w2

M is the mass of one person.
I = 1600 kg*m^2 is the merry-go-round moment of inertia (without people on it).
Solve for w2