Newton’s Laws and Linear Momentum: Difference between revisions
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====Multiple Particles==== | ====Multiple Particles==== | ||
The momentum of a system of particles is the sum of both particles' momentum (momenta). If the particles have masses | The momentum of a system of particles is the sum of both particles' momentum (momenta). If the particles have masses {{math|''m''<sub>1</sub>}} and {{math|''m''<sub>2</sub>}}, respectively, and velocities {{math|''v''<sub>1</sub>}} and {{math|''v''<sub>2</sub>}}, 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 14:43, 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 Template loop detected: Template:Math and Template loop detected: Template:Math, respectively, and velocities Template loop detected: Template:Math and Template loop detected: Template:Math, 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
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Simple
Middling
Difficult
Connectedness
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- How is it connected to your major?
- Is there an interesting industrial application?
History
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See also
- http://www.physicsbook.gatech.edu/Velocity
- http://www.physicsbook.gatech.edu/Mass
- http://www.physicsbook.gatech.edu/Vectors
- http://www.physicsbook.gatech.edu/Newton%E2%80%99s_Second_Law_of_Motion
Further reading
Chabay, Sherwood. (2015). Matter and Interactions (4th ed., Vol. 1). Raleigh, North Carolina: Wiley.
External links
References
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