Question

an ice skater spins in place at 4.6 revolutions/second while holding her arms in to her body such that her moment of inertia is 1.40 kgm2. she then extends her arms such that her moment of inertia increases to 2.60 kgm2 and applies a stopping moment of force to reduce her angular velocity (i.e. opposite to direction of rotation). determine the work done by this stopping moment in reducing her spin to 1 revolution/second

Answer 1

To calculate the work done by the stopping moment in reducing the skater's spin to 1 revolution per second, use the formula Work = (Change in angular kinetic energy) / (Change in angular velocity).

Step-by-step explanation:

When the ice skater extends her arms, her moment of inertia increases from 1.40 kgm² to 2.60 kgm². The stopping moment of force applied in the opposite direction of rotation reduces her angular velocity from 4.6 revolutions/second to 1 revolution/second. To calculate the work done by the stopping moment, we can use the formula:

Work = (Change in angular kinetic energy) / (Change in angular velocity)

Plugging in the values, we get:

• Change in angular kinetic energy = (1/2) * (Moment of inertia) * (Change in angular velocity)²
• Change in angular velocity = (Final angular velocity) - (Initial angular velocity)

Substituting the given values, we can calculate the work done by the stopping moment.