In lacrosse, a ball is thrown from a net on the end of a stick by rotating the stick and forearm about the elbow. If the angular velocity of the ball about the elbow joint is 30.0 rad/s and the ball is 1.30 m from the elbow joint, what is the velocity of the ball?

Solution:

The linear velocity, v and the angular velocity, \omega of a rotating object are related by the equation

v=r\omega

From the given problem, we have the following values: \omega=30.0 \ \text{rad/s} and r=1.30 \ \text{m} . Substituting these values in the formula, we can directly solve for the linear velocity.

\begin{align*}
v & =r\omega \\
\\ 
v & = \left( 1.30 \ \text{m} \right)\left( 30.0 \ \text{rad/s} \right) \\
\\
v & = 39.0 \ \text{m/s}\ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}