Main Ideas for Newton’s 3 rd law and Momentum
Newton’s 3 rd law says forces come in pairs that are equal and opposite.
If you push down on the ground with your feet, the ground pushes back up at you. If you push a box, the box pushes back at you with equal and opposite force. What you feel is the box pushing back at you.
Momentum (p) requires mass and velocity. An object not in motion has no momentum.
Momentum is mass times velocity p = mv units are kgm/s
Velocity is a vector and therefore cares about direction. Because momentum relies on velocity, it too is a vector quantity and direction matters. Momentum can be negative, zero, or positive (zero meaning not moving or stopped) and change in momentum can be negative, zero, or positive(zero meaning no change) p + ,  p + (car accelerates from 40 mph to 60 mph) p + ,  p - (car slows from 60 mph to 40 mph) p - ,  p - (soccer ball rolling at you gets kicked at you) p - ,  p + (wad of paper thrown at you bounces off)
An impulse is a force applied over a time. F  t Net force times change in time
Impulses change momentum and therefore impulse equals change in momentum so F  t =  p
You should be familiar by now with the symbol  (delta), which means change. Usually by change we mean subtraction between 2 values so  p = p f
- p i
(always final minus initial!!!) p f
meaning final momentum, p i
meaning initial momentum
Change in momentum can also be caused by a change in velocity  v (and remember a change in velocity is an acceleration which are caused by forces which is what an impulse is, but you already knew that). So we can also say  p = m  v but using what we know above we can combine ideas to say F  t =  p = m  v
Momentum is conserved. This means that the total momentum of all objects before a collision, or before an impulse, must equal the total momentum of all objects after the collision or impulse so……
total momentum before p i
= p f
total momentum after
Sum of object momentums before p
1
+p
2
= p
1
` + p
2
` sum of object momentums after
Objects initial mass X initial velocity (m
1 v
1
+ m
2 v
2
) = (m
1 v
1
` + m
2 v
2
`) objects final mass X final velocity
Collisions can be elastic (don’t stick together) or inelastic (stick together)
For elastic collisions, each object will have its own momentum before and after (equation above)
For inelastic collisions, objects will combine to make a new object and mass m
1 v
1
+ m
2 v
2
= (m
1
+ m
2
) v`
Sometimes total momentum before is zero and so total momentum after must also be zero. Before a bullet is fired, neither the gun nor bullet is moving, so there is no initial momentum. After the bullet is fired, the momentum of the bullet forward is equal and opposite to the recoil felt backwards through the gun. The momentum of the bullet forward, an object with small mass and large velocity, will be positive, and the momentum of the gun backward, an object with large mass and small velocity, will be negative.
Each momentum will be of equal size and opposite direction, therefore adding to zero total momentum.