Question

A gymnast does cartwheels along the floor and then launches herself into the air and executes several flips in a tuck while she is airborne. If her moment of inertia when executing the cartwheels is 13.5 kg·m² and her spin rate is 0.5 rev/s, how many revolutions does she do in the air if her moment of inertia in the tuck is 3.4 kg·m² and she has 2.0 s to do the flips in the air?

a) 2.5 rev
b) 3.0 rev
c) 3.5 rev
d) 4.0 rev

Answer 1

To find the number of revolutions the gymnast does in the air, we can use the conservation of angular momentum. The gymnast does approximately 2.0 revolutions in the air.

Step-by-step explanation:

To find the number of revolutions the gymnast does in the air, we can use the conservation of angular momentum. The initial angular momentum is equal to the final angular momentum. The initial moment of inertia is 13.5 kg·m² and the spin rate is 0.5 rev/s. The final moment of inertia is 3.4 kg·m² and we have 2.0 s to do the flips in the air. Using the formula for conservation of angular momentum, we can calculate the final spin rate:

Initial Angular Momentum = Final Angular Momentum

(Initial Moment of Inertia) * (Initial Spin Rate) = (Final Moment of Inertia) * (Final Spin Rate)

Plugging in the values, we have:
(13.5 kg·m²) * (0.5 rev/s) = (3.4 kg·m²) * (Final Spin Rate)

Simplifying the equation, we find:
6.75 rev = (3.4 kg·m²) * (Final Spin Rate)

Dividing both sides of the equation by (3.4 kg·m²), we get:
Final Spin Rate = 6.75 rev / (3.4 kg·m²) = 1.98 rev/s

Therefore, the gymnast does approximately 2.0 revolutions in the air.