# Physics of Figure Skating

### By: Zach Theile and Alexis McCarn

## Friction

The ice has a minimal friction that the skater utilizes to maintain momentum and velocity. This allows the skater to glide with out the friction of the contact between the ice-skate and the ice to restrict his/her motion.

This relates to the first law of Newtonian Physics:

**An object in motion tends to stay in motion unless acted on by an opposite, external force.**

## Momentum

The momentum of the skater allows for the skater's mass to carry kinetic energy along the ice, increasing the skater's linear inertia. The energy that is carried over the skater's mass through momentum is conserved and converted throughout the skater's path. Thusly, momentum is always conserved as well.

*Angular momentum:* the mass of the body rotating around it's center of gravity in which determines the location of the object's axis of rotation which depends on both the speed of rotation and the distribution of the weight of the mass around that axis. When the skater spins, the skater's arms are held in to aid in the positive acceleration of the skater's speed, which slows when the skater's arms are extended (and allows the skater's mass to be distributed over greater space), conserving constant momentum.

**Equation: **L(angular Momentum) = I(rotational inertia) * w(rotational speed)

Torque, defined as: The force of the angular momentum, or the momentum of a spinning object.

## Rotational Inertia

Equation: I(moment of inertia)= m(mass) * r(radius)^2

This uses the inverse square law (if the distance of the a mass from the axis of rotation doubles, the moment of inertia quadruples).

Since inertia is the resistance of a mass to force producing movement, this equation explains how the distance of her arms affects the speed of her rotation directly as the distance of her arms from her mass's centroid, and gravitational axis, is greater and proportionally decreasing it's resistance to her centripetal force.