Momentum and Uniformly Accelerated Motion – Concepts
Discussion of Principles
This document is largely for N students. This week's lab should be a very straightforward application of the Momentum Principle for M students, but may not be as familiar for N students. The following very briefly covers the main ideas.
Momentum Principle
First, we will define a useful physical concept known as momentum, a quantity related to an object's motion and inertia. At speeds not close to the speed of light, momentum is defined as where p is the object's momentum, m is its mass, and v is its velocity. One of the most-used equations in your N course will be Newton's 2nd Law, which you will get to very soon if you haven't already. It's typically expressed as where Fnet is the vector sum of all forces acting on a particular object, m is the object's mass, and a is the acceleration of the object resulting from the net force. Recalling that the instantaneous velocity of an object can be defined asa =
and the average velocity can be defined as | dv |
| dt |
aave =
,
we see that we can easily re-express equation 2 as
or
For situations with a constant net force, Newton's 2nd Law tells us that the acceleration must also be constant, and so equation 4 can simply be written as
Since we've defined momentum as | Δv |
| Δt |
p = mv,
this becomes
an alternative formulation of Newton's 2nd Law, and the equation known as the Momentum Principle in the M course. This will be the main equation used in the lab today.