A small playground merry-go-round is a uniform disk of mass and radius

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A small playground merry-go-round is a uniform disk of mass

150\,\text{kg}

and radius

1.6\,\text{m}

. A child standing next to the device pulls on a rope that is wrapped around its rim, producing an external torque that varies with time according to

\tau(t) = (12\,\text{N}\cdot\text{m/s}^{2})t^2

for

0 \le t \le 3.0\,\text{s}

. The merry-go-round is initially at rest. (a) Derive an algebraic expression for the change in the merry-go-round’s angular momentum between

t = 0

and

t = 3.0\,\text{s}

in terms of the given quantities. (b) Calculate the numerical value of the angular momentum change over the

3.0\,\text{s}

interval. (c) Determine the angular speed of the merry-go-round at

t = 3.0\,\text{s}