Chapter 11, Problem 017 A yo-yo has a rotational inertia of 844 g-cm* and a mass

Question

Chapter 11, Problem 017 A yo-yo has a rotational inertia of 844 g-cm* and a mass of 106 g. Its axle radius is 2.92 mm, and its string is 123 cm long. The yo-yo rolls from rest down to the end of the string. (a) What is the magnitude of its linear acceleration? (b) How long does it take to reach the end of the string? As it reaches the end of the string, what are its (c) linear speed, (d) translational kinetic energy, (e) rotational kinetic energy, and (f) angular speed? (a) Number (b) Number (c) Number (d) Number (e) Number (f) Number Units Units Units Units Units Units

Explanation / Answer

a) Linear acceleration, a = g[1 - I/(mr^2 + I)] = 981[1 - 844/(106*0.292^2+ 844)] = 10.39 cm/sec^2

b) t = ?[2L/a] = ?[2*123/10.39] = 4.86 sec

c) Vmax = a*t = 50.547 cm/sec

d) Et = 0.5m*Vmax^2 = 0.0135 J

f) wmax = Vmax/r = 0.50547/0.0029 = 174.3 rad/sec

e) rotational KE = 0.5 x 844 x (50.547/0.292)^2 = 1.26 x 10^7 ergs = 1.26 J

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