Answer
(a) The disk should turn at a rate of 1.91 rpm.
(b) $\alpha = 0.980~rad/s^2$
(c) $\theta = 2.60~rad$
$\theta = 149^{\circ}$
Work Step by Step
(a) The radius $r$ of the disk is $1.25 ~m$
One revolution of the disk is a distance of $2\pi ~r$.
$0.250~m/s$ is $15.0~m$ per minute.
$rpm = \frac{15.0~m}{(2\pi)(1.25~m)}$
$rpm = 1.91$
The disk should turn at a rate of 1.91 rpm.
(b) $\alpha = \frac{a}{r} = \frac{\frac{1}{8}~(9.80~m/s^2)}{1.25~m}$
$\alpha = 0.980~rad/s^2$
(c) $\theta = \frac{d}{r} = \frac{3.25~m}{1.25~m}$
$\theta = 2.60~rad$
We can convert this angle to degrees.
$\theta = (2.60~rad)(\frac{180^{\circ}}{\pi ~rad})$
$\theta = 149^{\circ}$
