### Question

Is the angle at which the object rebounds, in a perfectly elastic collision, from the surface equal to that at which it is incident?

Asked by: Andy

### Answer

Yes, if spin and/or frictional forces are ignored the incoming angle of the object
equals the angle at which it bounces from the surface. The angle, however, should be
measured in relation to a NORMAL line. That line is drawn perpendicular to the
surface at the point of impact. A normal line allows the rule to work for
curved surfaces as well as planes.

This behavior 'mirrors' the behavior of a light ray reflecting from a polished
surface. In addition to the 'angle of incidence equals the angle of reflection'
rule, the reflected path also lies in the same plane as the original path of the
object.

Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor

If you attempt to apply the idea that rebound angle
equals incident angle in the real world, you must take into account the
coefficient of restitution, the spin of the ball before the collision, and
the frictional coefficients (both sliding and rolling) to model the
situation. So in the real world the answer is that the rebound angle is
almost never equal to the incident angle.

Answered by: Phil Freedenberg, E.E.D., Exec. VP, Federal Engineering, Inc., Fairfax, VA