Momentum is equal to the mass multiplied by the velocity: $\vec{p} = m\vec{v}$. The SI units for momentum are kilogram meters per second (kg*m/s). Momentum can be used to determine both the direction and speed of colliding objects.
Check out this short video about the Momentum.
What is Momentum?
Read the BoxSand Introduction and watch the pre-lecture videos before doing the pre-lecture homework or attending class. If you have time, or would like more preparation, please read the OpenStax textbook and/or try the fundamental examples provided below.
There is a big difference between a bicycle traveling at 15 mph and a fire truck traveling with the same speed. The truck would be of more interest as it would be much harder to stop. The quantity that scales the velocity of an object by it's mass is called momentum.
$\vec{p} = m \vec{v}$
This realationship allows for small objects moving quickly to have the same momentum as large objects moving slowly. Also notice that momentum is a vector quantity because velocity is a vector quantity. Momentum and velocity must point in the same direction because they are connected by mass, a scalar.
If you are to change the momentum of a system you are going to either change its direction, or magnitude, or a combination of both. An example might be hitting a softball that is lobbed towards you. The velocity of the ball, and thus momentum right before the ball is hit is directed down an angle $\theta$ from the horizontal. After the hit, the velocity (and thus momentum) is increased and has changed directions, angled $\phi$ up from the horizontal in almost the opposite direction. A vector operation diagram describing the change in momentum (Impulse), is below.
This is a representation of two vectors if the initial and final momentum. The initial momentum arrow starts at some point and goes in some angle theta from the horizontal and the final momentum arrow starts at the same place of the tail of the initial momentum and points at some different location at an angle psi. The change in momentum starts at the head of the initial momentum to the head of the final momentum. The change in momentum is denoted as delta p vector which is equal to impulse denoted as j vector
The Impulse-Momentum Theorem states that the change in momentum (impulse) of a system is equal to the average net external force acting on the system multiplied by the change in time the force was applied.
$\vec{J}=\Delta{}\vec{p} = \Sigma{}\overline{\vec{F}}_{external}\Delta t$
In 1D, the graphical representation of the change in momentum (impulse) is equal to the area under a net force as a function of time curve. In 2 and 3D, each component of the change in momentum is equal to the area under the force component in that direction as function of time curve. An example could be the softball that was hit by a bat. The ball (and bat to some degree) deform when they collide. As they compress, the normal force between them increases. A plot of the more realistic x-force component as a function of time is shown below.
This a graph of the net force over time as a bell curve. the area underneath the curve is equal to the impulse.
The area under that curve is the impulse imparted to the ball in the x-direction. Sometimes it is modeled more simplistically with an average constant force as a function of time. If both curves have the same area then both will have imparted equal impulse to the ball.
Momentum
Impulse-Momentum Theorem
Now, take a look at the pre-lecture reading and videos below.
