As shown in Fig. E10.20, a string is wrapped several times around the rim of a small hoop with radius 0.0800 m and mass 0.180 kg. The free end of the string is pulled upward in just the right way so that the hoop does not move vertically as the string unwinds.

(a) Find the tension in the string as the string unwinds.

(b) Find the angular acceleration of the hoop as the string unwinds.

(c) Find the upward acceleration of the hand that pulls on the free end of the string.

(d) How would your answers be different if the hoop were replaced by a solid disk of the same mass and radius?

Figure E10.20:

Rolling down (a) a perfectly rigid surface and (b) a deformable surface. The deformation in part (b) is greatly exaggerated.

(a) Perfectly rigid sphere rolling on a perfectly rigid surface

(b) Rigid sphere rolling on a deformable surface

Mg Normal force produces no torque about the center of the sphere. Mg Normal force produces a torque about the center of the sphere that opposes rotation.