# Momentum

Watch this to unpack mass in motion for Higher Physics (and don’t let your guard down)

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Here’s a question: what do billiards and boxing have in common?

At first glance, it would seem like not a lot: In the first, you are trying to pot balls in pockets; in the second, you are trying to land punches on your opponent (and doing your best to avoid theirs)

Yet, there is a lot in common and the answer is actually pretty simple.

Both sports are defined by collisions, and their outcomes. How things collide – balls or boxing gloves – matters and so we need to understand the principles of momentum.

The ‘science of things colliding’ has an incredible array of real-world applications, from reducing plane and train crash deaths to designing the next nuclear warhead.

In simple Physics terms, we know it as ‘mass in motion’.

Let’s unpack it.

This is thinkfour.

Momentum is simple; we take an object’s mass and multiply it by its velocity – it doesn’t really matter whether we are talking about a boxing glove or a billiard ball. The outcome of this is the objects momentum in kgm/s. So a 80kg person running at 5m/s has a momentum of 80x5 – 400kgm/s.

So why do students lose marks on such a seemingly straight forward concept? The answer is that we often deal with two objects colliding and we need to take into account both of their momenta, and here is the absolutely most important thing to remember … Momentum is a vector and it must be conserved! So what do we mean by that? Well it means that as a vector direction matters, so if things are moving towards each other the outcome is different than if one is stationary and the other crashes into it!

What does “it must be conserved” mean? Simply put, the sum (that’s all of them added up) of all the objects momentum before the collision is EQUAL to the sum of their momentum after the collision.

Let’s consider two objects moving towards each other with an identical speed and mass but in the opposite direction. What are their respective momenta? Object 1 has mass 5kg and velocity 10 m/s to the right. Object 2 has mass 5kg and velocity 10 m/s to the left. Before the collision the sum of their momentum if we consider that object 2 is travelling in the opposite direction and is therefore a negative… is zero.

After the collision what happens? Both objects will stop dead in their tracks as their momenta essentially cancel each other out. The sum of momenta after the collision is therefore zero! So momentum is conserved.

What about if one of the objects is stationary? Say if a rugby player is standing ready to make a tackle on a player charging towards them. If assume that the defender clings onto the player running at them when they make the tackle, we can consider them as one big joined up object after the collision.

So if a 100kg person is sprinting at 6 m/s at a stationary 80kg person what is the momentum before the collision? The 100 kg person has a momentum of 600 kg m/s before the collision however the stationary person has a velocity of zero therefore has a momentum of zero. So the total momentum before and after the collision will be 600 kgm/s.

After the collision if the smaller 80kg person is hanging on for dear life we can now take them as one big object of mass 180kg and crucially they will both be travelling at the same speed if they are attached.

Therefore after the collision we will have 180kg of mass that must have momentum equal to 600 kgm/s. So our calculation is just 600 divided by 180. Which gives us a new velocity of 3.3 m/s in the direction the 100kg player was running to begin with.

So remember, Momentum is mass multiplied by velocity, it is a vector quantity, it must be conserved (the sum of all momenta must be the same before and after the collision).

The principles of mass in motion hold up on any terrestrial scale – so understanding momentum will help you reduce collisional impacts in plane or train crashes, or make the next bunker-busting missile be even more deadly.

Or if it’s just the effect of a collision of a billiard ball or a boxing glove you are trying to predict, this stuff matters.

(though it is perhaps more important to fully understand the impact of the boxing glove….)

This was thinkfour, thanks for watching.