An ice skater is spinning on frictionless ice with her arms extended outward. She then pulls her arms in toward her body, reducing her moment of inertia. Her angular momentum is conserved, so as she reduces her moment of inertia, her angular velocity increases and she spins faster. Compared to her initial rotational kinetic energy, her final rotational kinetic energy is (a) the same (b) larger, because her angular speed is larger (c) smaller, because her moment of inertia is smaller.

An ice skater is preparing for a jump with turns and has his arms extended. His moment of inertia is 1.8 kg·m² while his arms are extended, and he is spinning at 0.5 rev/s. If he launches himself into the air at 9.0 m/s at an angle of 45° with respect to the ice, how many revolutions can he execute while airborne if his moment of inertia in the air is 0.5 kg·m²?

A figure skater is spinning at 10.0 rad/s with her arms extended. Her rotational inertia is 2.50 $\mathrm { kg } \cdot \mathrm { m } ^ { 2 }$. After pulling her arms in, her rotational inertia is 1.60$\mathrm { kg } \cdot \mathrm { m } ^ { 2 }$. How much work does she do to pull her arms in while spinning?

Ballet A ballet student with her arms and a leg extended spins with an initial rotational speed of $1.0 \mathrm{rev} / \mathrm{s}$.As she draws her arms and leg in toward her body, her rotational inertia becomes $0.80 \mathrm{kg} \cdot \mathrm{m}^{2}$ and her rotational velocity is $4.0 \mathrm{rev} / \mathrm{s}$.Determine her initial rotational inertia.

An electric clock is hanging on a wall. As you are watching the second hand rotate, the clock's battery stops functioning, and the second hand comes to a halt over a brief period of time. Which one of the following statements correctly describes the angular velocity $\omega$ and angular acceleration $\alpha$ of the second hand as it slows down? (a) $\omega$ and $\alpha$ are both negative. (b) $\omega$ is positive and $\alpha$ is negative. (c) $\omega$ is negative and $\alpha$ is positive. (d) $\omega$ and $\alpha$ are both positive.

A figure skater is spinning with an angular velocity of + 15 rad/s. She then comes to a stop over a brief period of time. During this time, her angular displacement is +5 .1 rad. Determine (a) her average angular acceleration and (b) the time during which she comes to rest.