Momentum, Impulse, and Circular Motion

Linear momentum and impulse

(Linear) momentum is the product of mass () and velocity (), and has units .

Impulse is the product of force () and time (), and has units .

The impulse-momentum principle states the impulse imparted by a force is equal to the change in momentum:

Force and velocity are both vector quantities, so momentum and impulse are also vector quantities. The direction should be show correctly using the appropriate sign.

If there are no external impulses, then the law of conservation of momentum applies:

Restitution

Collisions range from perfectly elastic to perfectly inelastic. In a perfectly elastic collision. no kinetic energy is lost from the system. In a perfectly inelastic collision, the two objects coalesce.

Collisions between spheres

For two smooth spheres, Newton's Experimental Law states that:

Where is the coefficient of restitution. For a perfectly elastic collision, , while for a perfectly inelastic1 collision, . For this course, .

When modelling collisions between spheres, the assumptions generally are:

The spheres are smooth
The impulse during the collision acts along the line of sphere centres
None of the spheres are spinning

Collisions between a sphere and a fixed plane

When a sphere collides with a fixed plane, momentum is not conserved because the wall does not usually move. Newton's Experimental Law still holds, so by considering :

Footnotes
1: Footnote on perfectly inelastic collisions
For this course, 'inelastic' is taken to mean 'perfectly inelastic', that is (this is mentioned in the specification).