When a ball hits a hard surface why must the bounce angle always equal the collision angle?

Question

It is common knowledge and obvious from observation that this is always the case but where does the physical reason lie? - in terms of contact, angular momentum etc.?

Would it also be the case with collisions involving non-spherical objects? - eg. a cube and a plane surface.

Answer 1

The case of the ball striking a hard surface is like a light beam striking a perfectly reflecting surface (a mirror). There is no loss of energy and the angle of reflection is equal to the angle of reflection, because the vertical component of the velocity just gets reversed and the horizontal component remains unaffeted, thus giving rise to the equal triangles.

In actual practice, a small amount of friction is always present and the horizontal component of the velocity is reduced and the collision is not perfectly elastic so the vertical component too is affected. so, the angle of reflection is slightly different. Exactly how it changes can only be worked out if we know the loss of energy due to friction and inelasticity or experimentally observed.

With a cube the surface area is much higher and hence even slight friction affects the angle.

Answer 2

This is actually NOT always the case. Friction plays a role in keeping this from occuring. Heck, even the spin on the ball makes the angles different. That's why curve balls curve.

If you removed friction so that the ball had no spin, then conservation of momentum would tell us that the angles must be the same.

The momentum in the x direction before and after would be exactly the same.

The momentum in the y direction would be equal but opposite, which is why the angles are the same.


The answer for your second question is yes and no. It all depends on where the object lands. If the cube hit perfectly flat against the plane, it would act just like a sphere. However, if one corner of the cube landed first, it would being to rotate and the spin would throw off the angles again.

*EDIT* - To the above poster. Momentum is NEVER lost. You are thinking of energy. Momentum is ALWAYS conserved, even when energy is lost due to friction.

Answer 3

Put simple - conservation of linear momentum.

Analysing the collision in terms of conservation of vertical and horizontal components of the momentum you can see that (in the idealised situation where no momentum is lost) then the component normal to the surface changes sign after the collision & the component parallel to the surface stays constant.

So the net result is a 'reflection' and the bounce angle is equal to the collision angle.