Question

The tape in a videotape cassette has a total
length 281 m and can play for 2 h. As the tape
starts to play, the full reel has an outer radius
of 45 mm and an inner radius of 12 mm. At
some point during the play, both reels will
have the same angular speed.
What is this common angular speed?
Answer in units of rad/s.

Answer 1

$$d=281\ m,t=2(3600)=7200\ s$$

$$v=\frac{d}{t}=\frac{281}{7200}=0.039\frac{m}{s}$$

$$r=0.5(0.012+0.045)=0.0285\ m$$

$$\omega=\frac{v}{r}=\frac{0.039}{0.0285}=1.4\frac{rad}{s}$$