Question

A softball player swings a bat, accelerating it from rest to 2.6rev/s in a time of 0.20s . Approximate the bat as a 0.90-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it.

Answer 1

To calculate the torque, we need to find the moment of inertia of the bat and the angular acceleration. The moment of inertia of a uniform rod can be calculated using the given mass and length. The angular acceleration can be calculated by dividing the change in angular velocity by the time. Finally, the torque can be calculated by multiplying the moment of inertia and the angular acceleration.

Step-by-step explanation:

To calculate the torque applied by the player to one end of the bat, we can use the equation:

Torque = Moment of Inertia * Angular Acceleration

First, we need to find the moment of inertia of the bat. Since the bat is approximated as a uniform rod, its moment of inertia can be calculated as:

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

Substituting the given values, we get:

Moment of Inertia = (1/3) * 0.90 kg * (0.95 m)^2

Next, we need to find the angular acceleration. The angular acceleration can be calculated using the formula:

Angular Acceleration = (Final Angular Velocity - Initial Angular velocity) / Time

Substituting the given values, we get:

Angular Acceleration = (2.6 rev/s - 0 rev/s) / 0.20 s

Now, we can calculate the torque by multiplying the moment of inertia and the angular acceleration:

Torque = (1/3) * 0.90 kg * (0.95 m)^2 * ((2.6 rev/s - 0 rev/s) / 0.20 s)

Calculating this expression gives us the torque applied by the player to one end of the bat.