# Problem: In softball, the pitcher throws with the arm fully extended (straight at the elbow). In a fast pitch the ball leaves the hand with a speed of 139 km/h.Find the rotational kinetic energy of the pitcher's arm given its moment of inertia is 0.720 kg⋅m2 and the ball leaves the hand at a distance of 0.600 m from the pivot at the shoulder (the ball is 0.156 kg).

###### FREE Expert Solution

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.

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

###### Problem Details

In softball, the pitcher throws with the arm fully extended (straight at the elbow). In a fast pitch the ball leaves the hand with a speed of 139 km/h.

Find the rotational kinetic energy of the pitcher's arm given its moment of inertia is 0.720 kg⋅mand the ball leaves the hand at a distance of 0.600 m from the pivot at the shoulder (the ball is 0.156 kg).