Momentum

"the impetus gained by a moving object; a product of an objects mass and velocity"

represented by the letter  $p$  

 $p=m\times v$  

has a direction and therefore CAN be negative

units for momentum are kilograms x meters per second or  $kg\cdot\frac{m}{s}$  

opposite of less-mentum

 $m=\frac{p}{v}$  

 $v=\frac{p}{m}$  

"an impetus that results from a force exerted on an object over time"

 $J$  represented by the letter

 $J=F\times t$  

has a direction therefore CAN be negative

units for impulse are Newtons x seconds or  $N\cdot s$  

momentum is what an object has; you can see it the same way you see velocity

impulse is what you do; you have to act (apply a force) in order for there to be impulse

Units for impulse are $N\cdot s$  

 $N$  are the units for force which come from Newton's Second Law which is  $F_{net_{ }}=m\times a$  

substituting in the units for each quantity we would see  $N=kg\times\frac{m}{s^2}$  

replace  $N$  in the units for impulse with  $kg\cdot\frac{m}{s^2}$  and get

 $\left(kg\cdot\frac{m}{s^2}\right)\cdot s$  

 $s$  cancels out another  $s$   which gives the final form of  $kg\cdot\frac{m}{s}$  

in equation form this looks like:  $J=\Delta p$  

change in momentum is the difference in momenta or $\Delta p=p_f-p_i$  

combining the last two lines gives:  $J=p_f-p_i$  

Just like the Work-Energy Theorem, impulse "adds" momentum to a system

momentum $\left(p\right)$  depends on mass and velocity and includes direction  

 $p=m\times v$  

Impulse  $\left(J\right)$  is an applied force over a period of time

 $J=F\times t$  

Impulse can be found by finding the change in momentum

 $J=\Delta p$  OR $J=p_f-p_i$