# The upper end of the string wrapped around the cylinder is held by a hand that is accelerated...

## Question:

The upper end of the string wrapped around the cylinder is held by a hand that is accelerated upward so that the center of mass of the cylinder does not move as the cylinder spins up. Find
(a) the tension in the string
(b) the angular acceleration of the cylinder, and
(c) the acceleration of the hand{eq}\left ( I = \frac{1}{2} m r^2 \right ) {/eq}

## Torque:

Torque is defined as the moment of force. This quantity signifies rotational acceleration. An absence of torque is considered as static equilibrium.

(A) Since the center of mass of the rod is not moving, the tension is equal to the weight of the rod, thus, we write:

{eq}T = mg {/eq}

(B) Using the equation for static equilibrium, we write:

{eq}TR = I\alpha \\ mgR = \frac{1}{2}MR^2\alpha \\ \alpha = \frac{2g}{R} {/eq}

(C) The acceleration of the hand is given as:

{eq}a_h = \alpha R \\ a_h = 2g {/eq}