The string in a yo-yo is wound around an axle of radius 0.520 cm. The yo-yo has

Question

The string in a yo-yo is wound around an axle of radius 0.520 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.366 kg and outer radius 1.99 cm. Starting from rest, it rotates and falls a distance of 1.36 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 1.36 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

Height energy lost = Kinetic energy gained

KE gained = translational KE + Rotational KE

KE = 0.5 . 0.366 . V^2 + 0.5 . (0.5 . 0.366 . 0.0199^2) . (V/ 0.00520)^2

KE = 0.183 .V^2 + 1.34 .V^2 =1.523 . V^2 J

?GPE = m . g . ?h = 0.366 . 9.8 . 1.36 = 4.87 J

4.87 = 1.523 V^2

V = 1.788 m/s

2) Time taken = distance fallen / average velocity

T = 1.36 / 0.894 = 1.521 s

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