Swinging Balls and Momentum
Date: Thursday, August 22, 2002
I was playing with a little desk toy with suspended ball
bearings and wondered what would happen if the balls were made of a
material that was infinitely rigid.
With any real object (like metal) isn't momentum transferred to the
opposite ball at the speed of sound of the material?
Would momentum be transferred instantaneously with "rigid" balls?
Momentum is not transferred at the speed of sound. The speed of sound is a
velocity (meters/second), not a rate of transfer of momentum
(kilogram.meters/second) per second. The rate at which momentum is
transferred from one object to the other equals the force between the
objects: how hard they push on each other.
Still, you are on the right track. Infinitely rigid balls would not
compress at all. As the balls meet, their motions would have to be reversed
instantaneously or the balls would have to "overlap". This requires an
infinite force and an infinite rate of momentum transfer, except for one
fact. Infinitely rigid does not mean infinitely strong, only impossible to
compress. For an infinite force to exist, both objects must be able to
endure an infinite force. When an object is too rigid, this causing a force
greater than it can endure, the object shatters. Unless the rigid objects
were truly infinitely strong, they would break. If they were both
infinitely strong, they would bounce off each other as other objects do.
The motions would be the same, but the time actually in contact would be too
short to measure.
If one were much stronger than the other, you would have an "armor piercing
shell" striking a tank. The shell gives much less than the tank armor. If
the shell has enough momentum, the armor gives enough to allow the shell to
Dr. Ken Mellendorf
Illinois Central College
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