## College Physics (4th Edition)

(a) The drum's angular speed is $0.556~rad/s$ (b) The drum has made 1.06 revolutions. (c) $f = 0.088~s^{-1}$
(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: $f = \frac{\omega}{2\pi} = \frac{0.556~rad/s}{2\pi} = 0.088~s^{-1}$