The yo-yo in Figure 19 is made up of two disks of radius r = 3 cm and an axle of radius b = 1 cm. Each disk has mass M₁ = 20 g, and the axle has mass M₂ = 5 g.

(a) Use the result of Exercise 47 to calculate the moment of inertia I of the yo-yo with respect to the axis of symmetry. Note that I is the sum of the moments of the three components of the yo-yo.

Exercise 47

Prove the formula for the right circular cylinder in Figure 18.

I_z = 1/2 MR²

(b) The yo-yo is released and falls to the end of a 100-cm string, where it spins with angular velocity ω. The total mass of the yo-yo is m = 45 g, so the potential energy lost is PE = mgh = (45)(980)100 g-cm²/s². Find ω using the fact that the potential energy is the sum of the rotational kinetic energy and the translational kinetic energy and that the velocity v = bω since the string unravels at this rate.

Transcribed Image Text:

R H