Is there any device that has, for a moment or so, zero momentum and possess kinetic energy?

Asked by: Ali Azfar

Answer

Yes, actually a lot of them. The only difficult case is one with a single particle with no internal structure, then you can't have zero momentum, and have kinetic energy. However, with things that contain more than one particle, it is simple to think of such a device.

Take, for example, two equal masses connected to two ends of a spring, and vibrating simultaneously in-and-out. At any time, since the momenta of the two masses are opposite and equal in magnitude, the total momentum of the 'device' is zero. However, each possesses kinetic energy, so the total kinetic energy of the system is non-zero.

Another example would be a box filled with gas (air, for instance). The total momentum is zero, since the box isn't going anywhere as a whole. However, the total kinetic energy of the molecules is not zero.

Such a situation is always the case, when the vector sum of the momenta of the pieces constituting the system is zero, but the individual momenta are not. It is obviously the case with any device that has parts in motion, but the device isn't going anywhere as a whole. In rotary devices, the device will have non-zero _angular_ momentum, but that is not part of the question, as in the first example, it is possible to have systems with zero momentum, _and_ angular momentum, which still posses kinetic energy. And they are not limited to a moment, and can be in that state indefinitely, given the proper conditions.
Answered by: Yasar Safkan, Ph.D. M.I.T., Software Engineer, Istanbul, Turkey