Friction causing an impulse I have a quick question about impulse supplied by friction during a collision.  Given this situation:

The small bullet hits and sticks to the ball above the center of mass, causing rotation. 
If there is friction between the surface and mass M, will the change in momentum in the system on the horizontal axis before and after the bullet strikes the mass M, equal the impulse exerted by the friction force? Given there is friction, will it always exert an impulse during the ball and the M mass collision?
 A: 
If there is friction between the surface and mass M, will the change in momentum in the system on the horizontal axis before and after the bullet strikes the mass M, equal the impulse exerted by the friction force?

We know that the rate of change in momentum of a system is determined by the net external force acting on that system.
$$\mathbf F_\text{ext}=\dot{\mathbf P}_\text{COM}$$
or
$$\Delta \mathbf P_\text{COM}=\int\mathbf F_\text{ext}\,\text dt$$
Since impulse $\mathbf J$ is defined as the change in momentum, we have
$$\mathbf J=\Delta \mathbf P_\text{COM}=\int\mathbf F_\text{ext}\,\text dt$$
If you take your system to be the bullet and the ball together, then the only net external force acting on the system arises due to friction (gravity and the normal force cancel out). Therefore, $\mathbf F_\text{ext}=\mathbf F_\text{fric}$. So that
$$\mathbf J=\Delta \mathbf P_\text{COM}=\int\mathbf F_\text{ext}\,\text dt=\int\mathbf F_\text{fric}\,\text dt=\mathbf J_\text{fric}$$
where $J_\text{fric}$ is the impulse caused by friction. Therefore, we see that the impulse applied by friction is in fact equal to the change in momentum of the system.

Given there is friction, will it always exert an impulse during the ball and the M mass collision?

As long as 
$$\int\mathbf F_\text{fric}\,\text dt=\mathbf J_\text{fric}\neq0$$
during the collision, friction does supply an impulse to the system.
