A 180-kg merry-go-round in the shape of a uniform, solid, horizontal disk of radius 1.50 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force would have to be exerted on the rope to bring the merry-go-round from rest to an angular speed of 0.400 rev/s in 2.00 s? (State the magnitude of the force.)
Force required
$\begin{array}{rcl}\tau & =& I\alpha \\ Fr& =& I\alpha \\ F& =& \frac{I\alpha}{r}\\ & =& \frac{\frac{m{r}^{2}}{2}\left(\frac{\omega}{t}\right)}{r}\\ & =& \frac{mr\omega}{2t}\end{array}$
Substitute
$\begin{array}{rcl}F& =& \frac{\left(180\text{kg}\right)\left(1.50\text{m}\right)\left(0.400\text{rev/s}\right)}{2\left(2.0\text{s}\right)}\left(\frac{2\pi \text{rad}}{1\text{rev}}\right)\\ & =& 154\text{N}\end{array}$