Question

In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her arms at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 cm in the record spin.

a) 246 rev/min
b) 290 rev/min
c) 312 rev/min
d) 376 rev/min

Answer 1

The new rotation rate of the ice skater with her arms extended would be approximately 246 rev/min.

Step-by-step explanation:

To calculate the new rotation rate of the ice skater when she extends her arms, we need to consider the principle of conservation of angular momentum. Angular momentum is calculated as the product of the moment of inertia and angular velocity. Since the skater can be approximated by a 45-kg rod with a specific moment of inertia in the record spin, we can use the formula:

angular momentum = moment of inertia × angular velocity

Initially, the skater achieves a record rotation rate of 342 rev/min. Given that her moment of inertia changes when extending her arms, we can equate the initial and final angular momentum to find the new rotation rate. By rearranging the equation, we have:

angular velocityinitial × moment of inertiainitial = angular velocityfinal × moment of inertiafinal

By substituting the given values and solving for the final angular velocity, we find that the new rotation rate would be approximately 246 rev/min (option a).