elastic collisions in 2 dimensions

Question 1

in an oblique impact of a smooth sphere with a smooth surface, how do the parallel and perpendicular components of the velocity change?

Answer 1

parallel to smooth surface - velocity does not change
perpendicular to surface - changes by a factor of the coefficient of restitution.

Question 2

when the velocities of the sphere and impulse/eqn of wall are given as vectors, how can you find the angles involved?

Answer 2

use scalar dot product:
a.b = IaI IbI cosx

Question 3

for an impact between 2 spheres, along which line does the impulse act?

Answer 3

along the line of centres

Question 4

how do the components of the velocities parallel to the common tangent change?

Answer 4

they are unchanged

Question 5

how do the components of the velocities parallel to the line of centres change?

Answer 5

change by the factor of the coefficient of restitution

Question 6

what other rule applies to the component of velocities parallel to the line of centres?

Answer 6

conservation of momentum