Question

If a skater decreases her moment of inertia by a factor of 8, what happens to her final angular velocity?

a. It increases by a factor of 8
b. It decreases by a factor of 8
c. It remains the same
d. It doubles

Answer 1

If a skater decreases her moment of inertia by a factor of 8, the angular velocity increases by a factor of 8 due to the conservation of angular momentum, provided no external torques are acting on the system.

Step-by-step explanation:

If a skater decreases her moment of inertia by a factor of 8, her final angular velocity will increase by a factor of 8. This is a consequence of the conservation of angular momentum, which states that the angular momentum of an isolated system remains constant if no external torques act on the system. Angular momentum (L) is the product of the moment of inertia (I) and angular velocity (ω), given by the equation L = I × ω. If the moment of inertia decreases and no external torques are applied, the system compensates by increasing its angular velocity to keep the angular momentum constant. For example, an ice skater spinning at 0.800 revolutions per second with her arms extended reduces her moment of inertia from 2.34 kg · m² to 0.363 kg · m² when she pulls her arms close to her body. Because her angular momentum must be conserved, her angular velocity increases correspondingly.