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## 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
p, with, vector, on top, equals, m, v, with, vector, on topp, with, vector, on top is momentum, m is mass, and v, with, vector, on top 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 20, start text, space, m, p, h, end text has less momentum than a freight train moving at 1, start text, space, m, p, h, end text.
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, start subscript, 1, end subscript and m, start subscript, 2, end subscript, with velocities v, with, vector, on top, start subscript, 1, end subscript and v, with, vector, on top, start subscript, 2, end subscript, we can write P, with, vector, on top, start subscript, start text, t, o, t, a, l, end text, end subscript, equals, p, with, vector, on top, start subscript, 1, end subscript, plus, p, with, vector, on top, start subscript, 1, end subscript, where p, with, vector, on top, start subscript, 1, end subscript, equals, m, start subscript, 1, end subscript, v, with, vector, on top, start subscript, 1, end subscript and p, with, vector, on top, start subscript, 2, end subscript, equals, m, start subscript, 2, end subscript, v, with, vector, on top, start subscript, 2, end subscript.

## Frame of Reference

Since v, with, vector, on top is a vector, momentum, p, with, vector, on top, is also a vector. As such, the frame of reference impacts how we determine velocity v, with, vector, on top, and thus momentum p, with, vector, on top. 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 2, m, v. 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 p, with, vector, on top or by P, with, vector, on top . You may sometimes see p, with, vector, on top for an individual mass and P, with, vector, on top for a system of masses.