Question

An athlete can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s. If the length of a uniform baton is 0.8 m and the mass is 0.5 kg, what is the torque needed to reach the angular velocity? Group of answer choices

Answer 1

To find the torque needed to reach the given angular velocity, use the formulas for moment of inertia and angular acceleration.

Step-by-step explanation:

To calculate the torque needed to reach the given angular velocity, we can use the formula:

Torque = Moment of Inertia * Angular Acceleration

The moment of inertia of a uniform baton rotating about one end can be calculated using the formula:

Moment of Inertia = (1/3) * Mass * Length^2

Plugging in the given values, we get:

Moment of Inertia = (1/3) * 0.5 kg * (0.8 m)^2 = 0.1067 kgm^2

Now, we can use the given angular velocity and the time to find the angular acceleration:

Angular Acceleration = Angular Velocity / Time = 12 rad/s / 0.5 s = 24 rad/s^2

Finally, we can calculate the torque:

Torque = 0.1067 kgm^2 * 24 rad/s^2 = 2.56 Nm