Does an impulse contribute to both linear and angular momentum?

[etotheipi]

As an analogue, if 5J of work is done on an object then the linear KE might increase by 2J and the angular by 3J, so the work is divided between the linear and rotational forms.

Now suppose there is a sphere sliding on a frictionless surface. If an impulse of magnitude 1Ns is applied to the edge of the sphere (in a small enough time interval so that it can be considered to be in one direction only), does the impulse divide between change in linear and angular momentum?

If not, then for instance if the sphere is of radius 1m, the angular impulse is 1Ns and the linear impulse is also 1Ns, which means the 'overall' momentum of the sphere increases by 2Ns.

The question arises from a sort of similar situation in part b) of question A1 under this link https://www.aapt.org/physicsteam/2019/upload/USAPhO-2018-Solutions.pdf, where the same impulse of friction has been applied to both the rotational momentum and linear momentum separately instead of splitting up.

Sorry if I'm missing anything obvious.

 

[Dale]

If not, then for instance if the sphere is of radius 1m, the angular impulse is 1Ns and the linear impulse is also 1Ns, which means the 'overall' momentum of the sphere increases by 2Ns.

Angular impulse would be torque times time, so the units would be Nms not Ns. So in this sense the situation between rotational KE and linear KE is very different. Both of those are different parts of the same thing with the same underlying units. But linear impulse and angular impulse are not parts of the same thing, they are different things with different units. You cannot add, subtract, split, or otherwise compare them.

 

[etotheipi]

Angular impulse would be torque times time, so the units would be Nms not Ns. So in this sense the situation between rotational KE and linear KE is very different. Both of those are different parts of the same thing with the same underlying units. But linear impulse and angular impulse are not parts of the same thing, they are different things with different units. You cannot add, subtract, split, or otherwise compare them.

Right yes that was quite sloppy of me! I suppose then if the force is of magnitude F, we get a linear impulse of F \Delta t in addition to an angular impulse Fr \Delta t. Which means that if the linear impulse is \Delta p, the angular impulse is r \Delta p.

 

[Dale]

Yes, assuming $r$ is constant during the impulse.