The Mystery of the Skater's Hands Speed

What determines the speed of a skater's hands when they are 130 cm apart?

Is it the angular velocity, moment of inertia, or conservation of angular momentum that affects the speed of the skater's hands?

The Role of Conservation of Angular Momentum

The speed of a skater's hands is determined by the conservation of angular momentum. When the skater pulls her arms in, her moment of inertia decreases, and her angular velocity increases, resulting in a higher speed for her hands. Let's dive deeper into this concept.

Understanding Angular Momentum

Angular momentum is a fundamental concept in physics that describes the rotational motion of an object. It is defined as the product of an object's moment of inertia and its angular velocity. In the case of the skater, the conservation of angular momentum plays a crucial role in determining the speed of her hands.

When the skater, with her arms outstretched, spins at 130 rpm, her angular velocity is constant. However, as she pulls her arms in, the moment of inertia of her body changes, affecting her angular velocity. According to the principle of conservation of angular momentum, the total angular momentum of a system remains constant unless acted upon by an external torque.

The Equation for Conservation of Angular Momentum

The conservation of angular momentum can be mathematically expressed as:

ω₁₁ * I₁₁ = ω₂₂ * I₂₂

Where:

- ω₁₁ and ω₂₂ are the initial and final angular velocities, respectively.

- I₁₁ and I₂₂ are the initial and final moments of inertia.

By rearranging the equation, we can calculate the final angular velocity, which also represents the speed of the skater's hands as she pulls her arms in. This relationship between moment of inertia, angular velocity, and conservation of angular momentum provides insight into the physics behind the skater's changing speed.

Therefore, the next time you see a skater gracefully spinning on the ice, remember that it is the conservation of angular momentum that determines the speed of her hands as she performs intricate moves.