A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 15.0 m/s at a distance of 0.410 m from the joint and the moment of inertia of the forearm is 0.5 kg·m2, what is the rotational kinetic energy of the forearm?

Question

A baseball pitcher throws the ball in a motion where there is rotation of the forearm about the elbow joint as well as other movements. If the linear velocity of the ball relative to the elbow joint is 15.0 m/s at a distance of 0.410 m from the joint and the moment of inertia of the forearm is 0.5 kg·m2, what is the rotational kinetic energy of the forearm?

Answer 1

ke=1/2 I w^2

you are given I
w=v*r, you are given v, and r.

Answer 2

To calculate the rotational kinetic energy of the forearm, we need to use the formula:

Rotational kinetic energy = (1/2) * moment of inertia * angular velocity^2

We are given the linear velocity of the ball relative to the elbow joint, which is 15.0 m/s, and the distance from the joint to the ball, which is 0.410 m.

The linear velocity can be related to the angular velocity using the following equation:

Linear velocity = distance * angular velocity

We can rearrange this equation to solve for angular velocity:

Angular velocity = Linear velocity / distance

Plugging in the given values, we have:

Angular velocity = 15.0 m/s / 0.410 m = 36.59 rad/s

Now we can substitute the values into the formula for rotational kinetic energy:

Rotational kinetic energy = (1/2) * 0.5 kg·m^2 * (36.59 rad/s)^2

Calculating this expression, we find:

Rotational kinetic energy = 0.5 * 0.5 kg·m^2 * 1,338.88 rad^2/s^2

Simplifying, we get:

Rotational kinetic energy = 335.4 J

Therefore, the rotational kinetic energy of the forearm is 335.4 Joules.

Answer 3

To find the rotational kinetic energy of the forearm, we can use the formula:

Rotational Kinetic Energy = (1/2) * Moment of Inertia * Angular Velocity^2

First, let's find the angular velocity of the forearm. We know the linear velocity of the ball relative to the elbow joint, and at a distance of 0.410 m, so we can use the following equation:

Linear Velocity = Angular Velocity * Distance

Angular Velocity = Linear Velocity / Distance

Angular Velocity = 15.0 m/s / 0.410 m

Angular Velocity = 36.59 rad/s

Now, we can substitute this value into the formula:

Rotational Kinetic Energy = (1/2) * Moment of Inertia * Angular Velocity^2

Rotational Kinetic Energy = (1/2) * 0.5 kg·m^2 * (36.59 rad/s)^2

Rotational Kinetic Energy ≈ 294.1 J

Therefore, the rotational kinetic energy of the forearm is approximately 294.1 Joules.