- #1
- 36
- 0
Main Question or Discussion Point
Why is the angle between products in non head on, perfectly elastic collisions always 90 degrees?
I think this is only true for two equal masses. You can get there like this:Why is the angle between products in non head on, perfectly elastic collisions always 90 degrees?
The recoils of the two products are always 90 degrees apart if both incident masses are the same. It is proved somewhere in Goldstein's book on Classical Mechanics. Both masses have to be equal, and one has to be stationary before the collision.Why is the angle between products in non head on, perfectly elastic collisions always 90 degrees?
You are correct. Just imagine what the velocities would be relative to an observer who is flying past at a speed, in the original frame, that is 100 times greater than either of the particles' speeds.This moving off perpendicularly thing seems to only be possible from the frame of reference where originally one of the particles are at rest. I'm not sure about angles being preserved under a frame transformation... because if I consider relative to K' the velocities are perpendicular, but relative to K I have to add the relative velocity between K' and K and this would imply that relative to K the velocities are not perpendicular. I don't know if I'm correct on this point.
...not true.If this holds true in the frame of reference where B is initially at rest, it has to be true in every frame, because angles are preserved under frame transformations.
Yeah you're right, angles between velocities are of course frame depended. What was I thinking. So it's 90° only when one mass is at rest. Still useful in billiard.Just imagine what the velocities would be relative to an observer who is flying past at a speed, in the original frame, that is 100 times greater than either of the particles' speeds.
I used to believe that billiad ball collisions were ideal two-body collisions. But 2/7 of the total kinetic energy of a billiard ball is rotational, not linear (translational) kinetic energy, because their moment of inertia is 2/5 mR^{2}.Yeah you're right, angles between velocities are of course frame depended. What was I thinking. So it's 90° only when one mass is at rest. Still useful in billiard.