Momentum and Conservation of Momentum - Prof. Brian N. Espino, Exams of Physics

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More motion topics

Momentum

momentum is equal to the product of an object’s mass and its velocity.

p = m v

150 kg offensive lineman runs 5 m/s

p = (150 kg)(5 m/s) = 750 kg m/s

90 kg running back runs 9 m/s

p = (90 kg)(9 m/s) = 810 kg m/s

The running back has more momentum.

Momentum

When two cars crash and stick together the momentum is conserved. The two cars will move together with the same final velocity.

m 1 v 1 + m 2 v 2 = (m 1 + m 2 )vf

Two cars of the same weight crash into each other. One of the cars was initially sitting still.

mv 0 + m(0) = (m+m)vf

vf = ½ v 0

The cars move together with half the velocity of the first car.

Momentum

We can use the equation on the previous slide to determine how fast a gun shoots.

By firing a bullet into a block and knowing the masses and the speed the block obtains after being shot, we can calculate how fast the bullet was shot.

This is easy to do as long as the block is a lot more massive than the bullet.

Momentum - rocket

Works the same as shooting a gun, except you

are continuously firing ‘bullets’ (expelling gas).

Gas gets momentum in one direction.

The rocket gets momentum in the opposite

direction.

Momentum - explosions

An explosion can be treated as a collision in

reverse.

First an object has a momentum.

After the explosion, all the momentums of the

individual fragments add up to the original

momentum.

Momentum

If you want to change the momentum of an object, an outside force is required.

F = p/ t

F t = p

F t is called an impulse.

Impulse equals the change in momentum

Rotational Momentum

• Rotational or angular momentum is the equivalent to momentum when we study rotating objects.

Rotational inertia – an objects tendency to resist changes in how fast it spins. This is the rotational analogy to mass. This is determined by how far the mass is from the rotation point.

angular velocity – the rate that an object spins.

Rolling motion

• Earlier we rolled some objects down a ramp.
• Round objects with different mass distributions (disk, ball, hoop) rolled down with different speeds.
• They have different rotational inertias. As they start rolling, different amounts of energy is needed for rotation that is taken away from translation.

Rolling motion

Race a hoop against a disk. (each of radius r)

All of the hoop’s mass is r away from the center.

Some of the disk’s mass is closer than r from center.

The hoop has more rotational inertia. Harder for the hoop to start rolling. Angular velocity of the hoop speeds up slower.