Question

A baseball pitcher throws the ball in a motion involving rotation of the forearm about the elbow joint. If the linear velocity of the ball relative to the elbow joint is 20.0 m/s at a distance of 0.480 m from the joint and the moment of inertia of the forearm is 0.500 kg·m^2, what is the rotational kinetic energy of the forearm?

a) 96 J
b) 120 J
c) 144 J
d) 180 J

Answer 1

The rotational kinetic energy of the forearm is approximately 172.3 J. None of the option is correct.

Step-by-step explanation:

The rotational kinetic energy of the forearm can be calculated using the formula:

Krot = (1/2) * I * w^2

Where Krot is the rotational kinetic energy, I is the moment of inertia, and w is the angular velocity. In this case, we need to find the angular velocity of the forearm:

w = v / r

Where v is the linear velocity and r is the distance from the joint. Plugging in the values, we get:

w = 20.0 m/s / 0.480 m = 41.67 rad/s

Now we can calculate the rotational kinetic energy:

Krot = (1/2) * 0.500 kg m² * (41.67 rad/s)^2 = 172.3 J

Therefore, the rotational kinetic energy of the forearm is approximately 172.3 J.