The string in a yo-yo is wound around an axle of radius 0.540 cm. The yo-yo has

Question

The string in a yo-yo is wound around an axle of radius 0.540 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.282 kg and outer radius 1.95 cm. Starting from rest, it rotates and falls a distance of 1.15 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. (a)

What is the speed of the yo-yo when it reaches the distance of 1.15 m? ________ m/s

(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.] ______s

Explanation / Answer

a

As change in kinetic energy = change in potential energy

mv2/2 + Iw2/2 = mgh

mv2/2 + (mR2/2)v2/2r2 = mgh

v2/2 + v2R2/4r2 = gh

v = 1.7313 m/s

b

As a = 2gr2/R2 = 1.503 m/s2

So using vf - vi = at

t = 1.7313/1.503 = 1.1519 s

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