# Unwinding hoop

1. Jun 5, 2005

### MAPgirl23

A string is wrapped several times around the rim of a small hoop with
radius r = 7.90x10−2 m and mass 0.175 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
** here I used the equation for I = MR^2

I = (0.175 kg)(7.90×10−2 m)^2 = 1.092×10−3 now how do I find
the tension?

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.

2. Jun 5, 2005

### OlderDan

From my reply to this same problem elsewhere. You obviously recognize some of this but so I don't have to retype it

Newton's second law requires that the acceleration of an object be proportional to the net applied force. Rigid bodies, like this hoop, are complicated because different parts of the object are moving and accelerating in different directions. Fortunately, a detailed analysis of the problem reveals that you can treat a rigid body in terms of the linear motion and the rotational motion separately. Linear acceleration of the center of mass of the object is proportional to the net appplied force, and angular acceleration about the center of mass is proportional to the net torque about the center of mass. You need to look at these separately

F = Ma
T = I(alpha)

recognizing that a relationship exists between one of the forces in the problem and the net torque.