Angular and Linear Kinematics

Just like displacement, there is a strong relationship between linear and angular velocity.  What the equation and illustration below demonstrates is that linear velocity of any point on a rotating body is proportional to the radius of rotation (r; distance that point is from axis of rotation) and the angular velocity of the rotating body.

  

The equation above explains so much about how to improve sport performance and answers many questions about sport.  For example, why do professional golf and baseball have regulations on club and bat length?  To help answer the question consider golf clubs of different lengths (r; same loft) swung with similar angular velocities (w).  Notice in the diagram below the linear impact velocity (v) will be greater for clubs with greater lengths.  Of course, a longer club could compromise your ability to swing the club with a high angular velocity (and accuracy) and this would then defeat the purpose of using a longer club to hit the ball.