classical mechanics - What is the initial angular momentum of a rigid body given an offset impulsed force?

What is the imparted angular momentum to a rigid body if the impulse force is offset by a distance $h$ from the center of mass and the imparted momentum from the center of mass is $mv$?

For a homogeneous sphere I said the imparted angular momentum is $L=mvh$, but I am not sure if that is correct.

Answer

When you have an impulse $F\Delta t$ (I prefer that notation over $m\Delta v$ because it allows impulse to be imparted without worrying about the mass of the thing giving the impulse), then

1. The momentum of the center of mass changes as though the impulse was applied there, so $$m\Delta v = F\Delta t$$


2. The angular momentum changes according to the torque imparted $$\Delta \vec{L} = \vec{F}\Delta t \times \vec{h}$$

So yes, you got it right.