The string in a yo-yo is wound around an axle of radius 0.475 cm. The yo-yo has

Question

The string in a yo-yo is wound around an axle of radius 0.475 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.210 kg and outer radius 1.55 cm. Starting from rest, it rotates and falls a distance of 1.08 m (the length of the string). Assume for simplicity that the yo-yo is a uniform circular disk and that the string is thin compared to the radius of the axle. Part 1 out of 2 (a) What is the speed of the yo-yo when it reaches the distance of 1.08 m? m/b) How long does it take to fall? [Hint: The translational and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius.]

Explanation / Answer

a) I = m r2 = 0.210 * (1.55 * 10-2 )2 = 5.05 * 10-5 kg.m2

w * 0.475/100 = v

From conservation of energy

m g h = I w2 + m v2 = [5.05 * 10-5 * (100 v / 0.475)2] + [0.210 * v2]

0.210 * 9.81 * 1.08 = (2.238 + 0.210) v2

v = 0.953 m/s

b) v2 = u2 + 2 a s

a = 0.9532 / (2 * 1.08) = 0.420

t = v / a = 0.953 / 0.420 = 2.27 s

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