Momentum and Inertia

Momentum Momentum = mass x velocity MV = P Momentum is inertia in motion. A moving object has more p than an object with less m. An object at rest has no p (v = 0)

Momentum If the p of an object changes, the m, v, or both MUST change. If the v changes, then the object is accelerating a produces F The greater the F, the greater the change in v

Impulse The F sustained for a longer period of time produces more ∆p. This relationship of F to t is called impulse. Impulse = F ∆t The greater the impulse, the greater the ∆p.

Impulse-Momentum relationship F ∆t = mv This relationship helps us to analyze situations where the p changes.

Bouncing When an object bounces off a surface, the impulse is greater. The impulse required to bring an object to a stop and then to throw it back again is greater than the impulse required merely to bring it to a stop.

Conservation of Momentum If you wish to change p, you must exert an impulse on it. The impulse must be exert on the object by something outside the object. When a cannon is fired, according to Newton’s 3 rd, the ball has an equal but opposite force to the cannon. Same thing with p (within the system of the cannon and the ball)…the overall p before and after do not change.

Conservation of Momentum Remember p is vector quantity (magnitude AND direction) If no net force or net impulse act on a system, the momentum of that system cannot be changed. Law of Conservation of Momentum In the absence of an external force, the momentum of a system remains unchanged.

Collisions The collision of objects clearly shows the conservation of p. Net momentum before collision = Net momentum after collision Two main types of collisions Elastic and inelastic

Elastic Collisions Elastic collision: When objects collide without being permanently deformed or without generating heat. Ex: billiard balls (pool); swinging balls apparatus The momentum from the first object is transferred to the second object (or vice versa).

Inelastic Collisions Inelastic collisions: When colliding objects become entangled or coupled together, thereby generating heat or disfigurement. The net p before the collision equals the net p after the collision Net (mv) before collision = Net (mv) after collision