In a tape recorder, the magnetic tape moves at a constant linear speed of 5.6 cm

Question

In a tape recorder, the magnetic tape moves at a constant linear speed of 5.6 cm/s. To maintain this constant linear speed, the angular speed of the driving spool (the take-up spool) has to change accordingly.


(a) What is the angular speed of the take-up spool when it is empty, with radius
r1 = 0.64 cm?

(b) What is the angular speed when the spool is full, with radius
r2 = 2.38 cm?

(c) If the total length of the tape is 100.8 m, what is the average angular acceleration of the take-up spool while the tape is being played?

Explanation / Answer

a. C=pi*D = 3.14 * (2*0.79) = 4.96 cm. V=5.6cm/s * 6.28rad/4.96cm = 7.1rad/s. b. C = 3.14 * (2*2.32) = 14.57 cm. V = 5.6cm * 6.28rad/14.57cm = 2.4rad/s.

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