## Angular Momentum (Rotational Momentum)

## Angular Momentum is...

Angular momentum, or rotational momentum, is a vector quantity, meaning it consists of both magnitude and direction. It measures rotational momentum of a rotating object. Angular momentum can be measured by multiplying the moment of inertia (l) and the angular velocity (w).

## The Law of the Conservation of Angular Momentum

The law of the conservation of angular momentum states that angular momentum of an object is conserved when no external torque is being applied to the object.

L = mvr

where:

**L = angular momentum****m = mass****v = speed****r = radius**

*L*=

*Iω*

where:

**L = angular momentum***I*= moment of intertia*ω*= angular velocity

## Angular Momentum in Figure Skating

Angular momentum is useful in analyzing the elegant spins of figure skaters. According to the law of the conservation of angular momentum, the angular momentum of an object will not change unless external torque is applied to the object. When spinning, a figure skater will bring his or her arms closer to his or her body in order to increase their angular velocity and rotate faster. This works out because when the moment of inertia (I in the equation directly above) is decreased by bringing the arms closer to the body (and the angular momentum will stay the same according to the law of the conservation of angular momentum), the angular velocity must increase.

When gliding along the ice, figure skaters do not have angular momentum (recall Newton's Laws of motion, the figure skater will continue in a straight line). So, in order to spin/jump, the skater must generate angular momentum. The skater must apply a force to the ice and the force that the ice puts on the skater in turn, will give the skater the angular momentum necessary for the jump/spin.

A figure skater wants a lot of total angular momentum during their spin to create many spins as possible, and they can do this by having a large moment of inertia at the beginning of their jump or spin. Then, they can decrease their moment of inertia during their spin or jump and create lots more angular velocity (since angular momentum is the product of moment of inertia and angular velocity and angular momentum is conserved; this means less moment of inertia, meaning more angular velocity). So, to start jumps and spins, a figure skater will spread out either their arms or legs to maximize their moment of inertia and they will pull in their limbs to create more angular velocity while they spin.

When gliding along the ice, figure skaters do not have angular momentum (recall Newton's Laws of motion, the figure skater will continue in a straight line). So, in order to spin/jump, the skater must generate angular momentum. The skater must apply a force to the ice and the force that the ice puts on the skater in turn, will give the skater the angular momentum necessary for the jump/spin.

A figure skater wants a lot of total angular momentum during their spin to create many spins as possible, and they can do this by having a large moment of inertia at the beginning of their jump or spin. Then, they can decrease their moment of inertia during their spin or jump and create lots more angular velocity (since angular momentum is the product of moment of inertia and angular velocity and angular momentum is conserved; this means less moment of inertia, meaning more angular velocity). So, to start jumps and spins, a figure skater will spread out either their arms or legs to maximize their moment of inertia and they will pull in their limbs to create more angular velocity while they spin.