Newton’s Laws and Linear Momentum: Difference between revisions

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===A Mathematical Model===
===A Mathematical Model===
====Single Particles====
====Single Particles====
Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude:
Linear momentum is a vector quantity, like  velocity, possessing a direction as well as a magnitude:
:<math>\mathbf{p} = m \mathbf{v}</math>
:<math>\mathbf{p} = m \mathbf{v}</math>
where p is the vector stating the object's momentum in the three directions of three-dimensional space, and where v is the three-dimensional velocity vector giving the object's rate of movement in each direction, and m is the object's mass.
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====
====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
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> \begin{align} p &= p_1 + p_2 \\
:<math> \begin{align} p &= p_1 + p_2 \\
&= m_1 v_1 + m_2 v_2\,. \end{align} </math>
&= m_1 v_1 + m_2 v_2\,. \end{align} </math>

Revision as of 14:37, 14 April 2016

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.

A Computational Model

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

Examples

Be sure to show all steps in your solution and include diagrams whenever possible

Simple

Middling

Difficult

Connectedness

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

History

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

See also

Further reading

Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 1). Raleigh, North Carolina: Wiley.

External links

References

This section contains the the references you used while writing this page

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