The string in a yo-yo is wound around an axle of radius 0.537 cm. The yo-yo has

Question

The string in a yo-yo is wound around an axle of radius 0.537 cm. The yo-yo has both rotational and translational motion, like a rolling object, and has mass 0.320 kg and outer radius 1.97 cm. Starting from rest, it rotates and falls a distance of 1.33 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 1.33 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)

conserving energy,

0.5*0.48*v^2+0.5*(0.5*0.48*0.0197^2)*v^2/0.00516^2 = 0.48*9.8*1.49

so, v = 1.88 m/s <------answer(a)

b)

mg - T = ma

T*r1 = (0.5*mr2^2)*a/r1

So, a = 9.8/(1+0.5*(0.0197/0.00516)^2) = 1.18 m/s2

time taken = 1.88/1.18 = 1.59 s <-------answer

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.