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# 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 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

$\begin{array}{rcl}\tau & =& I\alpha \\ Fr& =& I\alpha \\ F& =& \frac{I\alpha }{r}\\ & =& \frac{\frac{m{r}^{2}}{2}\left(\frac{\omega }{t}\right)}{r}\\ & =& \frac{mr\omega }{2t}\end{array}$

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