MomentumChapter 9

Impulse and Momentum Recall that we defined linear acceleration to be:

Substitute this into Newton’s 2nd Law () and rearrange:

The quantity is called the impulse. The product is called the momentum and is written .

The impulse-momentum theorem is that the impulse is equal to the change in momentum:

Applications

Science of Speed: Momentum

Example Problem

9-4 A driver accelerates a 240 kg snowmobile, which results in a force being exerted that speeds up the snowmobile from 6 m/s to 28 m/s over a time interval of 60 s.b. What is the snowmobile’s change in momentum? What is the impulse on the snowmobile?c. What is the magnitude of the average force that is exerted on the snowmobile?

Angular Momentum In the case of rotational motion we saw that a statement of

Newton’s 2nd Law for rotation was:

We can rearrange this to read: . The quantity is the angular impulse and we can write the

right-hand side to be:

We can define the angular momentum to be:

So the angular impulse-angular momentum theorem is:

Conservation of Momentum We saw that to change the momentum of an object we can exert

an impulse on it. The force or impulse must be exerted by an object outside the

object. So if no net force or net impulse acts on a system, the

momentum of the system will not change. This is the law of conservation of momentum.

Laws of Conservation of Momentum

Law of conservation of linear momentum: If no external force acts on a system, the linear momentum of

that system does not change.

Law of conservation of angular momentum: If no external torque acts on a system, the angular

momentum of that system does not change.

Collisions

Collisions of objects demonstrate the conservation of momentum:

Two types of collisions Elastic: Objects collide without permanent deformation or without

generating heat. Inelastic: Objects become tangled or couple together.

Example Collision Problem

During a goal-line stand, a 75-kg fullback moving eastward with a speed of 8 m/s collides head-on with a 100-kg lineman moving westward with a speed of 4 m/s. The two players collide and stick together, moving at the same velocity after the collision. Determine the post-collision velocity of the two players.

Momentum Before Collision

Momentum After Collision

FullbackLinemanTotal

Example Problems 9-13 Two freight cars, each with a mass of 3 x 105 kg, collide

and stick together. One was initially moving at 2.2 m/s and the other was at rest. What is their final speed?

9-14 A 0.105-kg hockey puck moving at 24 m/s is caught and held by a 75-kg goalie at rest. With what speed does the goalie slide on the ice?

A disc with moment of inertia 1 kg·m2 spins about an axle through its center of mass with angular velocity 10 radians/s. An identical disc which is not rotating is slid along the axle until it makes contact with the first disc. If the two discs stick together, what is their combined angular velocity?

Conservation of Angular Momentum

Angular Momentum Conservation Demo Aerial Skiing Cat Video Ice Skating Circus Physics Angular Momentum on the ISS

Linear Momentum Demonstrations

International Space Station Momentum in Football Circus Physics Science of NFL Football

Lab Simulations

Collision Carts – complete worksheets for: Elastic Collisions Inelastic Collisions

Time permitting, try other simulations on this page