Is the velocity of a baseball pitcher's arm 100 MPH if his pitch is clocked going that fast?
Asked by: M. O'Connor
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
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'