# Linear Momentum Essay

In this module, we will learn how to describe the translational motion of a system of extended objects using the center of mass and momentum conservation. In general, such systems will also have two other types of motion: overall rotational motion and internal motions. We will deal with internal motion and rotation in later modules.

Momentum

We define the linear momentum (p) of a particle of mass m travelling at a velocity v as: p ⃗ = mv ⃗

Momentum is a vector quantity, and its unit is kg-m/s.

A particle either at rest or in constant velocity motion, will maintain a constant momentum. But if the particle is at rest or in constant velocity motion, there are no forces acting on it (Newton’s 1st law). When a force acts on the particle, its momentum will change over

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What is the maximum change in momentum for an 80 kg passenger on this elevator? What is the net change in the passenger’s momentum for the entire trip?

Answer: a) 1000 kgm/s; b) 0

Conservation on Momentum on Collision

The concept of momentum is particularly useful to understand and predict the outcome of a collision. Suppose that two point particles that are isolated from all interactions other than with themselves have a collision. If they collide, they must have been moving along a line connecting them either toward each other or in the same direction with one particle “catching up” to the other.

Before the collision, the particles move independently and do not interact; at that time each particle has its own momentum, p1 and p2. When they collide, they each exert a force onto the other and they change their momentum.

F ⃗1 on 2= (dp ⃗1)/dt and F ⃗2 on 1= (dp ⃗2)/dt

By Newton’s 3rd law of motion, we know that the force that one exerts on the other is the same and opposite as the force that the other exerts on the one, that is:

F ⃗1 on 2= F ⃗2 on 1

Hence (dp ⃗1)/dt = (dp