- #1

omega5

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## Homework Statement

As shown in the figure, a string is wrapped several times around the rim of a small hoop with radius R and mass M. 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.

## Homework Equations

##\tau=I\alpha##

##\tau=FR##

##I=MR^2##

##\Sigma F = ma##

## The Attempt at a Solution

Assumptions:

The tangential acceleration of the string is equal to the tangential acceleration of the hoop, which is essentially rolling along the string. This acceleration is due to a net force given by ##F_h-F_T##, where ##F_h## is the force exerted by hand and ##F_T## is the tension force.

The torque (and angular acceleration) will be greater than zero and negative (clockwise) since ##F_h>F_T##.

The net force acting on the center of mass is zero.

What force acts at the center of mass to keep the hoop in equilibrium? Getting stuck on this part has prevented me from understanding the situation enough to solve for tension, angular acceleration or the force exerted by the hand.