the tape in a videotape cassette has a total

length 256 m and can play for 2.3 h. As the
tape starts to play, the full reel has an outer
radius of 38 mm and an inner radius of 13 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.

1 answer

the common radius will be (38+13)/2 = 25.5 mm
The tape speed is 256m/2.3h = 30.9 mm/s
Now you should be able to figure the angular speed, knowing the circumference and linear speed. Think of the units involved.