A solid cylinder of mass 10 kg and radius 1.0 m rotates about its own symmetry axis. A rope wrapped around it exerts a 5.0-N force tangent to the cylinder, causing the cylinder to rotate clockwise. A second rope wrapped around another section of the same cylinder exerts a 6.0-N force that is tangent to the cylinder, causing the cylinder to rotate counterclockwise. The magnitude of the cylinder's angular acceleration is A) 0.20 rad/s². B) 0.91 rad/s². C) 1.1 rad/s². D) 10 rad/s². E) 11 rad/s².

Question

Quizplus · Accepted Answer

The net force exerted on the cylinder is the difference between the two forces due to the opposite directions of rotation they cause, which is $6.0\,N - 5.0\,N = 1.0\,N$. The torque ($\tau$) caused by this net force is given by $\tau = rF = 1.0\,m \times 1.0\,N = 1.0\,Nm$. The moment of inertia ($I$) of a solid cylinder rotating about its symmetry axis is $I = \frac{1}{2}MR^2$, where $M$ is the mass and $R$ is the radius. Substituting the given values, $I = \frac{1}{2} \times 10\,kg \times (1.0\,m)^2 = 5.0\,kg\cdot m^2$. The angular acceleration ($\alpha$) is given by $\alpha = \frac{\tau}{I}$, so $\alpha = \frac{1.0\,Nm}{5.0\,kg\cdot m^2} = 0.20\,rad/s^2$.

A Solid Cylinder of Mass 10 Kg and Radius 1