Question

A playground merry-go-round has radius 2.40m and moment of inertia 2100kg?m2 about a vertical axle through its center, and it turns with negligible friction.

A child applies an 22.5N force tangentially to the edge of the merry-go-round for 19.0s . If the merry-go-round is initially at rest, what is its angular speed after this 19.0s interval?

How much work did the child do on the merry-go-round?

What is the average power supplied by the child?

Answer 1

Note that

Torque = F r

Thus, as F = 22.5 N, r = 2.40 m,

Torque = 54.0 m*N

As

Torque = I (alpha)

--> alpha = Torque / I

where I = moment of inertia = 2100 kg*m^2

alpha = angular acceleration

Thus,

alpha = 0.0257 rad/s^2

As

w = wo + alpha * t

and

wo = initial angular velocity = 0 rad/s
w = final angular velocity
t = time = 19.0 s

Then

w = 0.4886 rad/s   [ANSWER, PART A, angular speed]

******************

Note that

Work = Torque (delta theta)

Here,

delta theta = wo t + 1/2 (alpha) t^2

Thus,

delta theta = 4.64 rad

Thus,

Work = 250.6 J   [ANSWER, PART B]

********************

Note that

Power = Work/time

= 13.2 W   [ANSWER, PART C]