What Is Momentum?

Momentum

What do you think of when you hear the word "momentum"? What does an object's momentum depend on?

Here's a short clip to start with.

It will auto-stop about a minute in. (This post is a mix of great moments from several video clips.)

Bill reminds us that momentum depends on how much mass an object has. Does momentum involve anything else?

So momentum depends on velocity too. Turns out that an object's momentum equals the product of its mass and velocity. In physics we usually call momentum $\vec{p}$, so we write $$\vec{p} = m\vec{v}.$$

Obviously, when an object changes its mass or velocity, its momentum changes as well. But what actually makes an object change its momentum? And what does a change in momentum necessarily imply? Think back to a basic and super useful law! Hint: what quantity is related to acceleration (which is related to velocity)?

Newton's Second Law of Motion! (we can use this because acceleration is the derivative of velocity.)

Well, looks like we've got a good basic understanding of momentum. Momentum will be useful to us throughout our study of mechanics, so this is a job well done. To celebrate, here are some entertaining examples of (too much) momentum:

A bullet has a small mass compared to a cricket ball. You'd still prefer being hit by a cricket ball rather than a bullet.

Why?

Because, it is not just mass that matters. Velocity is important too.

We use a physical quantity called momentum for this purpose.

Momentum is just Velocity multiplied with Mass.

Since, velocity is a vector, momentum is a vector too.

Does light have momentum?

Light has a speed of about 300,000,000 meters per second. Now although it has such a high speed, light has no mass. Light is not transmitted in waves, or particles. It is a special case called photons, which is kind of a mix between the two. Now, the exact details are something I am not entirely sure of. It involves some terms such as Planck's Constant and Einstein's laws of energy, and this is where my knowledge about this ends.

Many websites have more information on this, but for people that know more about this feel free to suggest edits/contribute to my explanation or create another lecture about this vast and difficult tangent for momentum.

The dictionary definition of what "momentum" is "the quantity of motion an object has". What really determines momentum is both mass and velocity. Without these two factors, it would be impossible to find out what momentum truly meant.

Momentum is a property of matter, such as mass and density, that conceptually refers to mass in motion. If you think about the use of the word momentum in everyday life, you may have heard something like "That team's momentum will pull it through the season" or more literally "The roller coaster's momentum kept it going through the second hill." This can tell you that momentum refers to how hard an object will be to stop.

Momentum is based on both mass and velocity, in the simple relationship Momentum is equal to mass times velocity, or p = mv. Therefore, its unit reflects this and the standard unit for momentum is kg • m/s. Let's try a practice problem on calculating momentum.

One very important thing to remember regarding momentum is that it is a vector quantity, similar to displacement or velocity, so a direction must be included in any answer with momentum.

What would be the effect on the momentum of the ball of mass M and Velocity V if the mass is doubled and the speed stays the same?

Show that when a billiard ball collides elastically with an identical stationary one, the angle between the resultant trajectories is $\frac{\pi}{2}$ radians. (Interesting Problem)