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### Course: High school physics - NGSS>Unit 1

Lesson 2: Introduction to momentum

# Introduction to momentum

Review your understanding of momentum in this free article aligned to NGSS standards.

## Key terms

TermMeaning
SystemThe collection of objects that are of interest. Systems can be closed or open, and they can be isolated or not isolated.
MassThe inertia of an object. The measure of an object’s resistance to change in motion.
VelocityThe rate of change of the position of an object. Velocity is a vector. The direction of the velocity is the direction of motion of the object, and the magnitude of the velocity is the speed of the object.
MomentumThe product of mass and velocity. Because velocity is a vector, momentum is also a vector.

## Equations

EquationSymbol breakdownMeaning
$\stackrel{\to }{p}=m\stackrel{\to }{v}$$\stackrel{\to }{p}$ is momentum, $m$ is mass, and $\stackrel{\to }{v}$ is velocityThe momentum of an object is the mass of the object multiplied by the velocity of the object

## Introduction to Momentum

Both the mass and velocity of an object impact momentum. As a result, less massive objects can have more momentum than more massive objects (if the less massive object is moving faster), and slower objects can have more momentum than faster objects (if the slower object has more mass). For example, a parked car has less momentum than a flying mosquito and a bicycle moving at has less momentum than a freight train moving at .
Depending on the situation, we can consider the momentum of individual objects, or we can consider the total momentum of an entire system. The total momentum of a system is the vector sum of all the individual masses that comprise the system. So for a system that consists of two masses, ${m}_{1}$ and ${m}_{2}$, with velocities ${\stackrel{\to }{v}}_{1}$ and ${\stackrel{\to }{v}}_{2}$, we can write ${\stackrel{\to }{P}}_{\text{total}}={\stackrel{\to }{p}}_{1}+{\stackrel{\to }{p}}_{1}$, where ${\stackrel{\to }{p}}_{1}={m}_{1}{\stackrel{\to }{v}}_{1}$ and ${\stackrel{\to }{p}}_{2}={m}_{2}{\stackrel{\to }{v}}_{2}$.

## Frame of Reference

Since $\stackrel{\to }{v}$ is a vector, momentum, $\stackrel{\to }{p}$, is also a vector. As such, the frame of reference impacts how we determine velocity $\stackrel{\to }{v}$, and thus momentum $\stackrel{\to }{p}$. For example, the passenger inside a moving car will have a momentum of $0$ with respect to the car, but their momentum is non-zero with respect to the ground.
In addition, for the chosen reference frame, the $x$-direction and the $y$-direction of the momentum for each object must be considered separately. For example, two objects with the same mass and speed moving in the same direction will have total momentum of $2mv$. But if those objects were moving directly towards each other, they would have a total momentum of zero.

## What else should I know about momentum?

• Momenta of zero. If an object is moving, its momentum cannot be zero. However, this is not necessarily true for a system. Since momentum is a vector, the total momentum of a system can be zero if there are multiple masses. For instance, a system of two objects that have the same magnitude of momentum and are moving directly toward one another will have a total momentum of zero.
• Momentum can be represented by $\stackrel{\to }{p}$ or by $\stackrel{\to }{P}$ . You may sometimes see $\stackrel{\to }{p}$ for an individual mass and $\stackrel{\to }{P}$ for a system of masses.

## Want to join the conversation?

• probably a stupid question to ask:-

why is momentum p?
• Some interpret the reason for keeping P as the symbol for momentum as the letter being derived from Latin word Petere which means ‘to go and seek’. This meaning is also related to the word ‘impetus’ which is the earlier term used for ‘momentum’. The word ‘impetus’ gives the meaning as to go and rush upon which was explained by the term Petere. Hence, momentum is represented by the letter P.
• Is the equation in the introductory paragraph right? Shouldn't it be P(total) = p1 + p2 instead of P(total) = v1 + v2?
• Yes I think the equation in the introductory paragraph is incorrect.
• why momentum is multiple of mass and velocity,

i mean we have feel that momentum should increase when either mass or velocity increase, so there can't be subtraction or division.

we could add both mass and velocity and the result will increase in that case too,

what decided that they should be multiple instead of other increasing operations like square or something,

or is this one of the special case of more bigger picture?
• That's because this is in fact a concept, just as in length there is no absolute "one", so what ever is the unit is just defined by the scientists. Through experiments they have determined that momentum is proportional to the mass of the object and its velocity, and proportion indicates that the relationship is multiplication instead of addition. You can also add a factor k, but in this case since this concept is quite isolated and does not need to be merged with other unit systems, simply multiplying is enough.
• How is velocity a vector?
(1 vote)
• A vector in physics is defined as something that has magnitude and direction.

Velocity has both. For instance, a car is traveling at 60 miles per hour in a southward direction.

60 mph is the magnitude
south is the direction.

thus, it is a vector.

speed just has magnitude, so if you say a car is traveling 60 mph, that is just speed.
• Under "what else should I know about momentum" it says "For instance, a system of two objects that have the same magnitude of momentum and are moving directly toward one another will have a total momentum of zero."- Would this still apply if both objects had different masses?
• Here the total momentum is zero because they have equal but opposite momentums, and if we add both of them they will be 0, but if we change the masses then their momentums would change, therefore the total momentum would not be 0.
For example if we have 2 cars both with a mass of 40kg and a velocity of 20m/s, then each of the cars would have a momentum of 800 kgm/s , but with different directions, so one of them, Object 1, would be 800kgm/s and another, Object 2, would be -800kgm/s , so when we add them we would get zero, but lets say object 1 has a mass of 30 kgs, then its momentum would be 600kgm/s, and if we add object 1's momentum with object 2's momentum, it would be a total momentum of -200kgm/s.
Hope this helps.
• why am i so depressed?
• In the What else should I know about momentum? section, was Momenta supposed to be momentum?