Question

Answer the following questions: Explain how skaters can quickly go from a slow to fast spin and vice versa. What happens to their angular velocity and moment of inertia? Is an external torque required? Explain.

Answer 1

Po:- Soln moment of inertia is, I = MRC m mass R Radius Also, angular momentum is, L = I w w angular speed This means, angular momentum depends on moment of inertia and angular speed. Thus, If a skater spins with their arms out and then brings their arms in the distance from the center is reduced and thus moment of inentia is decreases. Now, as moment of inertia and angular speed has inverse relation as shown in the equation (i = 10), so the skater spins faster to maintain the angular momentum. Similarly, if the skater put their arms out, radicus increases. This result in the increase in moment of inertia and thus decrease in angular speed. Thus, the skater slows down. - As described / explained above, Angular velocity → increases moment of inertia decreases I In case when the skater spins L with their arms Angular relocity moment of inertia decreases - Increases In case when the skater spins with their arms out

sont The only external force involved in a skater's spin. is friction with the ice and the ais. with As explained earlier, when the skater goes into a spin, she has a certain angular momentum. When. she puts her dress in, she will speed up, conserving angular momentum. Similarly, by extending her arms, she will slow down for the same reason. Thus, nothing else is needed, no external storque is required. The skates's rotational en kinetic energy increases/decreases because she does work pulling in/out her arms.