A.2.3. Impulse and Momentum

● Momentum: The product of an object's mass and velocity. p⃗=mv⃗ a{p} = m ext{v}

Momentum is a measure of an object's motion, calculated by multiplying its mass (how much 'stuff' it has) by its velocity (how fast it's moving in a specific direction). This means that a heavier object moving at a certain speed will have more momentum than a lighter object moving at the same speed.

Imagine trying to push a shopping cart. A full cart (more mass) is harder to push than an empty one, even if you push both at the same speed. The full cart has more momentum due to its larger mass.

● Impulse: The change in momentum resulting from a force applied over a time interval. J⃗=Δp⃗=F⃗Δt a{J} = Δ ext{p} = ext{F}Δt

Impulse refers to the effect of a force applied to an object over a certain period of time, which results in a change in the object's momentum. Mathematically, impulse can be calculated by multiplying the force applied to an object by the time duration for which the force is applied. Thus, the greater the force or the longer it is applied, the more the object’s momentum can change.

Think of a basketball player taking a shot. The longer the player forces the ball with their hand (more time applied), or the harder they push (more force), the greater the speed (and therefore momentum) the ball has when it leaves their hands.

Impulse is equal to the change in momentum of an object.

The key relationship here is that impulse is directly responsible for changing momentum. If you apply an impulse to an object (by exerting a force for a specified time), that object's momentum will change according to the impulse applied. This foundational principle is crucial in understanding how objects behave when forces act on them.

Consider a car coming to a stop. The brakes exert a force over a period of time (the impulse), causing the car’s momentum (which depends on its speed and mass) to decrease until it stops completely.

In a closed system with no external forces, the total momentum before and after an interaction remains constant. ∑p⃗initial=∑p⃗final a{∑ ext{p}{ ext{initial}}} = ∑ ext{p}{ ext{final}}

The principle of conservation of momentum states that when no external forces are involved, the total momentum of a system remains unchanged. This means that whatever momentum exists before an event (like a collision) will still be present after the event, although it can be distributed differently among the objects in the system.

Imagine two ice skaters pushing off of each other on a perfectly frictionless ice surface. They may move apart after the push, but if you measure their total momentum before and after they push off from each other, it will be the same, illustrating how momentum is conserved.

--