How to Calculate the Ice Skater's Speed After Pulling in Weights
What is the ice skater's initial spinning speed and how can we calculate her new speed after pulling in the weights in?
The ice skater spins around on the tips of her blades while holding a 5.0 kg weight in each hand. She begins with her arms straight out from her body and her hands 140 cm apart. While spinning at 2.0 rev/s, she pulls the weights in and holds them 50 cm apart against her shoulders. If we neglect the mass of the skater, how fast is she spinning after pulling the weights in?
Calculating the Ice Skater's New Speed
The new spinning speed of the skater can be calculated by using the principles of Conservation of Angular Momentum.
Angular Momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant if no external torques act on it. In the case of the ice skater spinning with weights, we can apply this principle to calculate her new speed after pulling in the weights.
To calculate the new speed, we first need to determine the moments of inertia before and after the weights are pulled in. The moment of inertia is a measure of an object's resistance to changes in its rotation speed.
Using the formula I = 2*(m*r²), where m is the mass of each weight (5.0 kg) and r is the distance of the weights from the axis of rotation, we can calculate the moments of inertia before and after the weights are pulled in.
After determining the moments of inertia, we can use the formula for angular momentum, which is given by L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
By applying the conservation of angular momentum, we can set the initial angular momentum equal to the final angular momentum and solve for the new angular velocity of the skater after pulling in the weights.
By following these steps and calculations, we can determine the new spinning speed of the ice skater and better understand the principles of angular momentum in rotational motion.