Force of Friction
Collisions
Conservation of linear momentum: If no external force acts on a system of masses, then its linear momentum remains constant.
Consider a system of masses m1, m2, m3, ..... moving with velocities v1, v2, v3, .... respectively. The net linear momentum of the system is:
If 
then 
constant.
Inf terms of X and Y components:
Head-on collision: If the initial and final velocities of colliding masses lie along the same line (along the common normal), then it is know as head-on collision.
From Law of conservation of momentum:
Oblique Collision
If the velocities of colliding masses are not linear, then it is known as oblique collision.
From Law of conservation of momentum:
Along X-axis:
Along Y-axis:
Coefficient of Restitution (Newton's Experimental Law)
(a) For direct impact: When two bodies collide head-on (direct impact), their velocity of separation after impact is in a constant ratio to their velocity of approach before impact and is in the opposite direction.
or 
The constant e is known as coefficient of restitution of two bodies.
Note: 
can be positive or negative or zero
(b) For oblique impact: When two bodies collide obliquely, their approach velocity resolved along their common normal after impact is in a constant ratio to their separation velocity before impact (resolved along common normal) and is in the opposite direction.
Elastic Impact: If there is no change in kinetic energy of the system, then the collision is known as elastic or perfectly elastic.
For an elastic collision:
Total KE before collision = Total KE after collision
For elastic impact: e = 1
For a perfectly inelastic impact (when the bodies stick together after impact): 
Oblique impact a smooth sphere against a fixed plane: A sphere of mass m collides with a fixed plane with initial speed u at an angle a with the normal. The sphere rebouds with speed v at an angle b with normal.
The plane being fixed, remains at rest.
...........(i)
Note: The downward component 
is negative.
As there is no force along the common tangent, the velocity (or momentum) of the sphere remains constant along that direction.
.............(ii)
Combining (i) and (ii), we get:
and 
Note : For a perfectly elastic collision, the above results are:
and 
For elastic collision, sphere rebound with same speed at same angle on the other side of the normal.
Direct impact of a smooth sphere against a fixed plane: If the sphere collides head on (directly) with the plane, 
Using the result of last section:
Rebound speed 
General equations for direct impact:If 
are velocities before impact of the masses 
and 
are the velocities after impact,
then we have
and 
Combining these equations, we get:
and
For a perfectly elastic collision, we can substitute e = 1.