Guide to Game Development/Theory/Physical motion/Momentum

This page is going to be relatively shorter than the other pages in this book. Simply because that momentum is such an easy part of physics and motion to grasp that any more writing would cause waffling. To understand this page you will need to have read up on Newton's second law from Newton's Second Law of Motion.

Understanding momentum
Momentum is used for collisions because we understand the Conservation of Momentum. Any object on the move has momentum and this can be used to determine many things about the object. For example, the force it experiences over a given time. The mathematical representation of momentum is as follows. $$p=mv$$

Conservation of Momentum
To understand momentum in collisions you must first understand that momentum is conserved before and after a collision. Also, when we are dealing with collisions, we are talking about one or more objects and each have their own momentum

This rules is what will appear in the next few parts when we talk about collisions and momentum.

Practical Equation
We can deduce from the statement above an equation. $$m_1u_1 + m_2u_2 =m_1 v_1 + m_2 v_2$$ Thus equation can be used for ALL types of collisions. However, there is a rule. If the objects are traveling in opposite directions, on velocity must be taken as negative.

Sticky Collisions
Sticky collisions mean that when two objects collide they coalesce and move off as one object after the collision. We can simplify the Conservation Equation for use with a sticky collision $$m_1u_1+m_2u_2=v(m_1+m_2)$$ The reason that we use only one final velocity is that the velocity after cannot be two different ones if they move off together after the collisions.

Impulse
$$ F=\frac{\Delta p}{\Delta t}$$ $$ F\Delta t = \Delta p $$ Impulse is really an extent of Newton's Second Law. Is works out the force experienced by an object in a given time. This is also equal to the change in momentum.