Final answer:
Using the conservation of angular momentum, a trapeze artist who reduces her rotational inertia to one third while rotating once per second would be able to increase her rotation rate to three rotations per second.
Step-by-step explanation:
If a trapeze artist reduces her rotational inertia to one third while rotating once each second, the new rotation rate can be calculated using the conservation of angular momentum. The conservation of angular momentum states that the angular momentum before and after a change must be equal if no external torques act on the system. Therefore, we can express this conservation with the formula L = L', where L is the initial angular momentum and L' is the final angular momentum. Angular momentum is the product of the moment of inertia (I) and angular velocity (ω), so L = I × ω and L' = I' × ω'. Given that the initial angular velocity is 1 rev/s and the final moment of inertia is one third of the initial, the final angular velocity ω' would be:
ω' = (ω × I) / I'
Since I' is one third of I, the relationship can be further simplified to:
ω' = 3 × ω,
which means that the final angular velocity is three times the initial angular velocity. So if she initially rotates at 1 rotation per second (rev/s), after contracting, she would theoretically be able to rotate at 3 rev/s.