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 22.3 22.3 m/s at a distance of 0.480 0.480 m from the joint and the moment of inertia of the forearm is 0.550 0.550 kg·m2, what is the rotational kinetic energy of the forearm?

rotational kinetic energy of the forearm is 593.6Joules

Explanation:

Rotational kinetic energy is expressed as shown

(K.E)r = 1/2Iω²

I is the moment of inertia

ω is the angular velocity

Given I = 0.550kgm²

ω = v/r

v is the linear velocity of the ball relative to the elbow

r is the distance

ω = 22.3/0.48

ω = 46.46rad/s

Rotational kinetic energy = 1/2×0.55×46.46²

= 0.55×1079.27

= 593.6Joules