Question

The tape in a videotape cassette has a total length 240 m and can play for 2.1 h. As the tape starts to play, the full reel has an outer radius of 47 mm and an inner radius of 11 mm. At some point during the play, both reels will have the same angular speed. What is this common angular speed?

Answer 1

total length of videotape = 240 m

total time of play = 2.1 h = 7560 s

so linear speed of the videotape is given as

$v = \frac{d}{t}$

$v = \frac{240}{7560} = 0.032 m/s$

now we know that

$v = r\omega$

here both reels have same speed when radius on both sides is same

so here

$r = \frac{r_o + r_i}{2}$

$r = \frac{47 + 11}{2} mm = 29 mm$

now from above equation we will have

$0.032 = 0.029\omega$

$\omega = 1.1 rad/s$