Question

A boy pulls on a string wrapped around the body of a top to make it spin. The string has a length of 57 cm and is wrapped around the top at a place where its radius is 1.6 cm. The top is initially at rest. He pulls the free end of the string, thereby unwinding it and giving the top an angular acceleration of +11 rad/s2 . Assume that the thickness of the string is negligible, and the rotational inertia of the top is 6.4 x 10-5 kg m2 . (a) How much angle displacement in rad does the top go thru when the string is completely unwound? (b) What is the final angular velocity of the top when the string is completely unwound? (c) How much torque is applied to the top? (d) How much work is done to the top?

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Answer 1

b.) S = RX0 = 57 cm. 6: 3t = 35.62 rad. 2 2 w²= 200 C in analogy with v3 u + 2as and u-o). so w?: 2x 11 X 35-62 w=5783.64 = 27.99 28 rad/sil a) Total angular displacement - 0 : (no. of revolcelion ) x C her L No. of revolcetion : circumference - 57 cm GA (1.6) an - 57 10.048 = 5.67 g rev. rev C.) ... = (5.672 ) ( 2K rad ) - (35.695 | radi To Id = 6:48 105 kg m² x ll rad, see? = 70.4 x105 ng m?s? d.) wood work done = ?XO - TO 4X105 x 35.695 - 2508x105]]