Final answer:
To calculate the final angular velocity of the twirler's baton, we can use the concept of angular momentum. By equating the initial and final angular momenta and solving for the final angular velocity, we can determine the rate at which the baton spins after the collision. The specific value depends on the moment of inertia, which was not given in the question.
Step-by-step explanation:
In this situation, we can use the concept of angular momentum to solve for the final angular velocity of the baton.
Angular momentum is the product of the moment of inertia and the angular velocity of an object. Mathematically, it is given by the equation:
Angular momentum = Moment of inertia × Angular velocity
Since energy is conserved in this scenario, we can equate the initial angular momentum to the final angular momentum:
Initial moment of inertia × Initial angular velocity = Final moment of inertia × Final angular velocity
Using the given values, we can substitute them into the equation and solve for the final angular velocity:
(0.762)(47.8) = (Final moment of inertia)(Final angular velocity)
Final angular velocity = (0.762)(47.8) / Final moment of inertia
Without knowing the specific moment of inertia of the twirler's baton, we cannot calculate the final angular velocity accurately. If the moment of inertia is provided, you can substitute that value into the equation to find the answer.