Answer
(a) The drum's angular speed is $0.556~rad/s$
(b) The drum has made 1.06 revolutions.
(c) $f = 0.088~s^{-1}$
Work Step by Step
(a) We can find the angular speed:
$\omega = \frac{v}{r} = \frac{0.50~m/s}{0.900~m} = 0.556~rad/s$
The drum's angular speed is $0.556~rad/s$
(b) We can find the angular displacement:
$\Delta \theta = \frac{d}{r} = \frac{6.0~m}{0.900~m} = 6.67~rad$
We can convert the angular displacement to revolutions:
$6.67~rad \times \frac{1~rev}{2\pi~rad} = 1.06~rev$
The drum has made 1.06 revolutions.
(c) We can find the frequency of rotation:
$f = \frac{\omega}{2\pi} = \frac{0.556~rad/s}{2\pi} = 0.088~s^{-1}$
