# Change in angular velocity of an initially non-rotating spherical object after a collision

In the theoretical scenario below:

Will the object rotate?

My first thoughts on this were:

The initial angular velocity is $$0$$. This means it does not have any angular momentum (right...?) and it theoretically will not rotate after the collision and it should not have any angular velocity (RiGhT?...) (due to conservation of momentum)? But that seems too good to be true as most objects should gain some form of rotation upon collision.

Then, I thought that maybe some of the impulse (upon collision) would be transferred to angular momentum and the rest to linear momentum, which is mostly going to cause it to rotate. Is my thinking correct here? If so, how do I calculate how much impulse is transferred into linear momentum and angular momentum?

• – gmz
Commented Oct 4, 2021 at 7:13
• @gmz this post kind of answers my question... I still do want to know whether the overall impulse in a collision is converted to both linear and angular impulse, and if so, how much to each of them. Commented Oct 4, 2021 at 7:31
• You can use the angular impulse equation $Δ\textbf{L} = \textbf{r}\times Δ\textbf{p}$ (which works because $\textbf{r}$ does not change during the collision) and conservation of energy.
– gmz
Commented Oct 4, 2021 at 7:44
• @gmz oh so its similar to linear impulse but related, thanks Commented Oct 4, 2021 at 8:15