Angular velocity, power and work

A playground merry-go-round has a radius of 4.40m and a moment of inertia of 255 kg*m^2 and turns with negligible friction about a vertical axle through its center.

1.)A child applies a 20.0N force tangentially to the edge of the merry-go-round for 22.0s . If the merry-go-round is initially at rest, what is its angular velocity after this 22.0s interval? (rad/s)

2.)How much work did the child do on the merry-go-round?(J)

3.)What is the average power supplied by the child?(W)

1.)A child applies a 20.0N force tangentially to the edge of the merry-go-round for 22.0s . If the merry-go-round is initially at rest, what is its angular velocity after this 22.0s interval. (rad/s)

torque = force x radius = 20 x 4.4 = 88 N.m

torque = inertia x alpha (rad/s^2, angular acceleration)

88/255 = alpha = 0.3451 rad/s^2

omega = alpha x time = 0.3451 x 22 = 7.6 rad/s (answer)


2.)How much work did the child do on the merry-go-round (J).

work done by torque = torque x distance in radians

torque = 88 N.m

distance = (omega initial + omega final)/2 x t = (0 + 7.6)/2 x 22 = 83.51 radians

88 x 83.51 = 7349.21 J (answer)


3.)What is the average power supplied by the child.

Power = work done/time

7349.21/22 = 334 Watts (answer)