Physics

Problem

A solid cylinder of mass

5.0\,\text{kg}

and radius

0.30\,\text{m}

can rotate freely about its central axis. A belt pulls tangentially on the outer rim with a

9.0\,\text{N}

force in the counterclockwise direction. Simultaneously, a rope wrapped around a smaller hub of radius

0.10\,\text{m}

exerts a

4.0\,\text{N}

tension that tends to rotate the cylinder clockwise. Find the angular acceleration of the cylinder and indicate its direction.