Question

The tape in a videotape cassette has a total
length of 223 m and can play for 2.3 h. As the
tape starts to play, the full reel has an outer
radius of 36 mm and an inner radius of 10 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

Answer:

1.2 rad/s

Explanation:

Assuming constant linear speed:

v = 223 m / (2.3 h × 3600 s/h)

v = 0.027 m/s

When the the reels have the same radius, they have the same angular velocity.  That happens halfway between full and empty.

r = (0.010 m + 0.036 m) / 2

r = 0.023 m

The angular velocity of both reels at that point is:

ω = v / r

ω = 0.027 m/s / 0.023 m

ω = 1.2 rad/s