Linear Momentum

AP Physics C

What is Momentum?

• What is its definition?

Momentum: the product of an object’s mass and its velocity

Momentum: “mass in motion”

Momentum: “quantity of motion”-Newton

Momentum: It is a vector!

Momentum: is sometimes called linear momentum

What is Momentum?

How do we calculate it?

What are its units?

mass length time

kgm

s

px mvxIf object is moving in arbitrary direction:

py mvy

pz mvz

Examples:

• Calculate the momentum of:

A) Calculate the momentum of a 5 kg object that is moving 3 m/s to the right? Left?

B) A 3.00 kg particle has a velocity of Find its x and y components of

momentum. Find the magnitude and direction of its momentum.

How is momentum related to other physics concepts that we have already studied?

We will soon see that it has many things in common with Energy, Newton’s 3rd law, and The Calculus.

The time rate of change of linear momentum of a particle is equal to the net force acting on the particle.

Pause to think about calculus concepts:• Why is a derivative involved?

• What does this say about the slope of a momentum-time graph?

• The area under which graph might be meaningful?

• So, how might an integral be involved?

Momentum may be changing non-uniformly with time

The slope of a momentum-time graph is net force!

The area under a force-time graph is a change in momentum!

The integral of force with respect to time is a change in momentum!

Pause to think about calculus concepts:

The integral of force with respect to time is a change in momentum!

We call the left-hand side of this equation the IMPULSE of the

force

Pause to think about calculus concepts:

The slope of a momentum-time graph is net force!

The area under a force-time graph is a

change in momentum or an

impulse

Examples• An object experience a net force that

varies with time such that: F(t) = 3t2 + 2t + 3. Find the impulse given to the object between the times of 0 and 3 seconds. Find the change in momentum.

• According to the graph below, what is the change in momentum of the 2.00 kg particle? If the particle originally has a speed of 2 m/s, what is its speed after the impulse is provided?

Impulse-Momentum Theorem:

The impulse of a force F equals the change in momentum of the particle.

This is another way of saying that a net force must be applied to change an objects state of motion.

Why does this look different from the

last equation?

Because the force might be constant!

A few things about IMPULSE:

It is a vector in the same direction as the change in momentum.

It is not a property of an object! It is a measure of the degree to which a force changes a particles momentum.

We say an impulse is given to a particle.

What are its units?From the equation we see that they must be the same as

momentum’s units (kgm/s).

Impulse approximation: assume the force is applied only for an instant and that it is much greater than other forces

present.

Things you should have seen from the Investigation.

Quick Conceptual Quiz

• Can a hummingbird have more momentum than a rhino?

• Why might an out of control truck hit a haystack or barrels and pile of sand as opposed to a wall as an emergency stop?

• How is a ninja’s ability to break stacks of wood related to impulse and momentum?

• What good is it to know an object’s momentum?

• When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard floor?

• No – the same impulse – the force exerted on the dish is less because the time of momentum change increases.

Example: Conservation of Momentum in Two Dimensions

Peregrine falcons often grab their prey from above while both falcon and prey are in flight. A 0.8 kg falcon, flying at 18 m/s, swoops down at 45˚ angle from behind the a 0.36 kg pigeon flying horizontally at 9.0 m/s. What are the speed and direction of the falcon (now holding the pigeon) immediately after impact?

Example: Conservation of Momentum in Two Dimensions

A 10 g projectile is traveling east at 2.0 m/s, when it suddenly explodes into three pieces. A 3.0 g fragment is shot due west at 10 m/s while another 3.0 g fragment travels 40˚ north of east at 12 m/s. What are the speed and direction of the third fragment?

Example: Conservation of Momentum in Two Dimensions

A firecracker traveling with a velocity of 3 m/s

in the direction of the +x axis, explodes and

breaks up into two equal pieces. After the

explosion, one piece flies off with a velocity of

2 m/s at an angle of 30 degrees above the

+x axis. Find the velocity of the second piece.