The tape in a standard VHS videotape cassette has a total length of 246 m, which

Question

The tape in a standard VHS videotape cassette has a total length of 246 m, which is enough for the tape to play for 2.0 h. As the tape starts, the full reel has a 45-mm outer radius and a 12-mm inner radius. At some point during the play, both reels have the same angular speed. Calculate this angular speed in radians per second and in revolutions per minute. Hint: Between the two reels the tape moves at constant speed.

rad/s rev/min The tape in a standard VHS videotape cassette has a total length of 246 m, which is enough for the tape to play for 2.0 h. As the tape starts, the full reel has a 45-mm outer radius and a 12-mm inner radius. At some point during the play, both reels have the same angular speed. Calculate this angular speed in radians per second and in revolutions per minute. Hint: Between the two reels the tape moves at constant speed.

Explanation / Answer

1. At the instant both reels have the same area, 2(Rf^2 - r^2) = R^2 - r^2

Solve for Rf

Rf

= 32.9 mm = 3.29 cm

1. Determine the linear speed v

2. Find w = v/r

v = 246/2 m/h = 123 m/h = 3.42 cm/s

w = 3.42/3.29 rad/s = 1.04 rad/s = 9.93 rev/min

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