The string in a yo-yo is wound around an axle of radius 0.524 cm. The yo-yo has

Question

The string in a yo-yo is wound around an axle of radius 0.524 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.169 kg and outer radius 1.59 cm. Starting from rest, it rotates and falls a distance of 1.11 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. What is the speed of the yo-yo when it reaches the distance of 1.11 m?
Hint--The translational and rotational kinetic energies are related, but the yo-yo is not rolling on its outer radius.

Explanation / Answer

Height energy lost = Kinetic energy gained KE gained = translational KE + Rotational KE KE = 0.5 . 0.169 . V^2 + 0.5 . (0.5 . 0.169 . 0.0159^2) . (V/ 0.00524)^2 KE = 0.0845 .V^2 + 0.389 .V^2 = 0.4735 . V^2 J ?GPE = m . g . ?h = 0.169 . 9.8 . 1.11= 1.84 J 1.84 = 0.4735 V^2 V = 1.97 m/s

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