Angular impulse can be calculated using the integral $\int \vec{\tau} dt$ or $\vec{\tau} \Delta t$ for a constant torque.

Calculate the angular momentum of each individual component relative to the axis of rotation, then add them together using superposition.

1. Identify if external torques are present. 2. If not, apply conservation of angular momentum: $L_{initial} = L_{final}$. 3. Calculate initial and final angular momenta. 4. Solve for unknowns.

1. Recognize that angular momentum is conserved ($L = I\omega$). 2. Use $I_1\omega_1 = I_2\omega_2$. 3. Solve for the final angular velocity $\omega_2$.

1. Calculate the angular impulse: $\vec{\tau} \Delta t$. 2. Set it equal to the change in angular momentum: $\Delta \vec{L} = \vec{\tau} \Delta t$. 3. Solve for the desired quantity.

The rotational equivalent of linear momentum; a measure of an object's resistance to change in its rotation.

A measure of an object's resistance to changes in its rotational speed about an axis of rotation. It depends on the mass and the distribution of mass relative to the axis.

A twisting force that tends to cause rotation. It is the rotational equivalent of linear force.

The change in angular momentum of an object. It is equal to the net external torque multiplied by the time interval over which the torque acts.

The sum of all torques acting on a system due to forces external to the system.

The rate of change of angular displacement with respect to time, typically expressed in radians per second.

It changes the object's angular momentum.

Their moment of inertia decreases, and their angular speed increases, conserving angular momentum.

The total angular momentum of the system is conserved.

The angular speed increases to conserve total angular momentum.

It changes the object's angular momentum.