Torque ($ au$) is a twisting force that causes rotation. It is the product of the force and the lever arm (the distance from the axis of rotation to the point where the force is applied).

Rotational inertia (*I*) is a measure of an object's resistance to changes in its rotational motion. It depends on the object's mass and how that mass is distributed relative to the axis of rotation.

Angular acceleration ($alpha$) is the rate of change of angular velocity with respect to time. It is measured in radians per second squared (rad/s²).

Net torque ($Sigma au$) is the sum of all torques acting on an object. It determines the angular acceleration of the object.

The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. It is a critical component in calculating torque.

1. Identify the force applied. 2. Determine the distance from the axis of rotation to the point where the force is applied (lever arm). 3. Calculate torque using the formula $\tau = rF\sin\theta$, where $\theta$ is the angle between the force and the lever arm.

1. Calculate the net torque ($Sigma \tau$) acting on the object. 2. Determine the rotational inertia (*I*) of the object. 3. Apply the formula $\alpha = \frac{\Sigma \tau}{I}$ to find the angular acceleration.

1. Perform a linear analysis to determine the linear acceleration of the center of mass using $\Sigma \vec{F} = m\vec{a}$. 2. Perform a rotational analysis to determine the angular acceleration about the axis of rotation using $\Sigma \tau = I\alpha$. 3. Relate linear and angular quantities if necessary (e.g., for rolling without slipping, *a* = *rα*).

1: Tension (T) upwards, 2: Weight (mg) downwards

1: Tension (T) tangential, 2: Weight (Mg) downwards, 3: Normal force (N) upwards

The hollow cylinder has a greater rotational inertia.