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.

The rotational equivalent of force; what causes an object to start rotating or change its rotation.

A measure of how much an object resists changes in its rotational motion.

The rate of change of angular velocity.

The net torque on an object is equal to the product of its rotational inertia and angular acceleration: $\sum \tau = I \alpha$.

The linear speed of a point on a rotating object, related to angular speed by $v = r\omega$.

The linear acceleration of a point on a rotating object, related to angular acceleration by $a = r\alpha$.

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*).