Question

A spinning ice skater with his arms straight out is rotating at 180 degrees per second. His moment of inertia, i, in this configuration is 3.0 kg-m². If he pulls his arms in and starts rotating at 360 degrees per second, what is his new moment of inertia?

Answer 1

When the ice skater pulls in his arms, his moment of inertia decreases and his rotational speed increases. The formula for moment of inertia is I = m * r^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation. In this case, since the skater's mass remains constant, the decrease in moment of inertia is due to the decrease in the distance from the axis of rotation when he pulls in his arms.

Step-by-step explanation:

When the ice skater pulls in his arms, his moment of inertia decreases and his rotational speed increases. The formula for moment of inertia is I = m * r^2, where I is the moment of inertia, m is the mass, and r is the distance from the axis of rotation. In this case, since the skater's mass remains constant, the decrease in moment of inertia is due to the decrease in the distance from the axis of rotation when he pulls in his arms. The initial moment of inertia, i, is given as 3.0 kg-m², and the initial rotational speed, omega, is given as 180 degrees per second. The new moment of inertia can be calculated using the formula I = i * (omega/omega')^2, where omega' is the new rotational speed. Plugging in the values, the new moment of inertia is i' = 3.0 * (180/360)^2 = 1.5 kg-m².