Sum the individual angular momentum vectors of each part of the system, considering both magnitude and direction.

By changing their moment of inertia (e.g., pulling arms in), they alter their angular speed to conserve angular momentum.

Angular speed increases.

If the net external torque on a system is nonzero, angular momentum is transferred between the system and its environment. The change in angular momentum equals the angular impulse from the net external torque over a time interval.

Check if the net external torque acting on the system is zero. If it is, angular momentum is conserved.

1. Identify the system. 2. Check for external torques. 3. If no external torques, apply conservation of angular momentum: L_initial = L_final. 4. Solve for the unknown variables.

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.

The total angular momentum of a closed system remains constant unless acted upon by an external torque.

Angular impulse is the product of the net torque and the time interval over which it acts. Units are $\text{kg} \cdot \text{m}^2/\text{s}$.

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

A system where no external torques act upon it, allowing angular momentum to be conserved.

The rotational equivalent of linear momentum. For a point particle, it is given by $\vec{L} = \vec{r} \times \vec{p}$, where $\vec{r}$ is the position vector and $\vec{p}$ is the linear momentum.