Rotational kinetic energy:

$\overline{){\mathbf{K}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{I}}{{\mathbf{\omega}}}^{{\mathbf{2}}}}$

where I is the moment of inertia and ω is the angular velocity.

Moment of inertial of a point mass:

$\overline{){\mathbf{I}}{\mathbf{=}}{{\mathbf{mr}}}^{{\mathbf{2}}}}$

Relationship between linear velocity and angular velocity.

$\overline{){\mathbf{\omega}}{\mathbf{=}}\frac{\mathbf{v}}{\mathbf{r}}}$

A softball pitcher throws an underhanded pitch with the arm fully extended (straight at the elbow). The ball leaves the pitcher's hand with a speed of 25 m/s. Assume that the pitching motion originates with the arm straight back and terminates with the arm straight down. Do not ignore gravity. Treat the pitcher's arm as a rod rotating about one end.

The ball has a mass of 0.755 kg and the moment of inertia of the pitcher's arm is 0.72 kg · m^{2}. Find the rotational kinetic energy of the pitcher's arm (including the ball) if the ball leaves the hand at a distance of 0.585 m from the pivot in the shoulder.

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