Newton’s Laws and Linear Momentum

Claimed by Patrick Todd

The Main Idea

Linear momentum is a vector quantity which is defined by the product of an object's mass, generally denoted as the lowercase "m", and its velocity (a vector), v. Linear momentum is represented by the letter "p" and is generally referred to as momentum for short.

A Mathematical Model

Single Particles

Linear momentum is a vector quantity, like velocity, possessing a direction as well as a magnitude:

[math]\displaystyle{ \mathbf{p} = m \mathbf{v} }[/math]

where p is the vector stating the object's momentum in the three directions of space, and where v is the three-dimensional velocity vector giving the object's movement in each of these directions, and m is the object's mass.

Multiple Particles

The momentum of a system of particles is the sum of both particles' momentum (momenta). If the particles have masses m₁ and m₂, respectively, and velocities v₁ and v₂, the total momentum is:

[math]\displaystyle{ \begin{align} p &= p_1 + p_2 \\ &= m_1 v_1 + m_2 v_2\,. \end{align} }[/math]

This model can be used to measure the momentum of a system of any amount of particles.

In Relation to Newton's Second Law

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

Simple

Find the momentum of a ball that has a mass of 69kg and is moving at <1,2,3> m/s.

Middling

A car has 20,000 N of momentum. How would the momentum of the car change if: a) the car slowed to half of its speed b) the car completely stopped c) the car gained its original weight in luggage

Difficult

Connectedness

How is this topic connected to something that you are interested in?
How is it connected to your major?
Is there an interesting industrial application?

History

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

Newton’s Laws and Linear Momentum

Contents