QUESTION #106

# Is the velocity of a baseball pitcher's arm 100 MPH if his pitch is clocked going that fast?

Asked by: M. O'Connor

### Answer

When a pitcher is preparing to throw the ball there is typically a 'wind-up' period. Once the pitcher gets the ball in motion she is effectively transferring momentum from her body to the ball. Hence it is not necessarily the case that her arm should move at the velocity the ball initially has. The amount of momentum transferred to the ball is thus more indicative of the velocity her arm has. To actually calculate this would be a rather involved procedure.
Answered by: Adrian Soldatenko, Undergraduate student at UCLA

You have asked about the velocity of the arm when the pitcher pitches the ball. It must be noted that it is meaningless to talk about the velocity of the arm as such. There is a special term for that, called angular velocity. The pitcher releases the ball. We assume that he does so at his fingertips. So, neglecting air resistance to the ball (which actually lowers the average velocity of flight), we conclude that it is indeed necessary that the velocity of the fingertips is equal to the linear velocity of the ball. The velocity of his fingertips is the resultant velocity, which is the vector sum of all his velocities that is the velocity due to angular motion, translation velocity, and also the velocity of the wrist, when it does the back and forth motion. And also remember that the central portion of the arm (the central point of the arm, about which the arm is rotating, there is only one velocity, which is transnational.

Transnational velocity loses meaning in Baseball, since that pitcher has to be stationary. But in Games like cricket, even the velocity of the bowler when he runs in has to be considered.
Answered by: Akhilesh, Student, GT, Vizag, India