Linear Momentum

The linear momentum p of an object

of mass m with a velocity of v is

It is a vector and points in the same

direction as the velocity vector.

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The momentum vector is an entirely

different vector than the velocity vector.

Care should be taken in comparing one to

the other.

It is safe to say that the momentum

vector is in the same direction as the

velocity vector as mentioned earlier.

One can also say that the momentum

vector is directly proportional to the

velocity vector, i.e., the momentum

vector doubles if the velocity vector

doubles.

But momentum also depends on the

mass.

So changing the mass of an object will

also change the momentum vector.

Therefore to change momentum one

must change the mass or velocity or

both.

Regardless of what changes, the

momentum vector is always in the same

direction as the velocity vector.

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As long as there are no external forces acting on a system of particles, collisions between the particles will exhibit conservation of linear momentum.

This means that the vector sum of the momenta before collision is equal to the vector sum of the momenta of the particles afterwards.

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This is known as the conservation of linear momentum.

It is an extremely important concept in physics.

One important area that makes use of this conservation principle is collisions.

This is what you are going to explore today.

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The collision you will study will involve two objects of equal mass colliding in a horizontal plane and then undergoing projectile motion after the collision.

Since the horizontal component of velocity remains constant for a projectile in free fall, the horizontal part of the projectile motion can be used to represent the horizontal component of the momentum after collision.

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Collision between two objects of the same mass. One mass is at rest.

Collision between two objects. One not at rest initially has twice the mass.

Collision between two objects. One at rest initially has twice the mass.

Simple Examples of Head-On Collisions

(Energy and Momentum are Both Conserved)

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Collision between two objects of the same mass. One mass is at rest.

Collision between two objects. One not at rest initially has twice the mass.

Collision between two objects. One at rest initially has twice the mass.

Simple Examples of Head-On Collisions

(Totally Inelastic Collision, only Momentum Conserved)

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Collision between two objects of the same mass. One mass is at rest.

Example of Non-Head-On Collisions

(Energy and Momentum are Both Conserved)

If you vector add the total momentum after collision,you get the total momentum before collision.

Velocity Components in Projectile Motion(In the absence of air resistance.)

Note that the horizontal component of the velocity remains the same if airresistance can be ignored.

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Here is an example of what you aregoing to do in the exercise today.

You will roll a balldown the curved ramp.

This represents the velocity as the ball left the tablebecause the horizontal velocity of a projectile remains constant in the absence of air resistance.