Momentum is a kind property that is sort of hard to pin down, but in general terms it is a property that relates to mass and velocity of a body (or object).

A body moving at a certain rate requires a certain amount of force to stop it. For example, a train travelling at 2 metres per hour is a lot harder to stop than a bullet travelling at 1000 metres per hour. This is due to the mass of the train being larger than the mass of the bullet. And if you were fixed in space, and you were hit by a train you would be instantly compressed. The only reason people survive being hit by cars and trains is due to a brief contact, in which a car or a train transfers its momentum to the person and sends it through space.

Momentum may be used in a video game when we want to simulate explosions that seem realistic. For example, when we blow a ship away, we may want to model the shock wave disturbing the other ships around it (Watch Star Wars Episode II and you'll see this effect). Therefore, we might want to do a momentum transfer, which may change the velocity of the other objects relative to their masses. The formula to compute momentum is the following:

momentum = mass * velocity

Since velocity is a vector quantity and mass is a scalar quantity, momentum is also a vector quantity.

Momentum on its own isn't that useful. You may be asking what are the uses of momentum. This is what I explain next in the law of Conservation of Momentum.

Conservation of Momentum

The law of conservation of momentum is used in the computation of collisions between objects. What that law states is that after a collision between two objects the momentum is conserved. It may be transformed, but it will still exist. But, momentum is only conserved if there is no friction in the game world, which would translate to loss. The formula for conservation of momentum is the following:

Where, m₁ is the mass of the first object, m₂ is the mass of the second object and V₁ and V₂ are the velocities of object 1 and object 2 respectively.

Momentum can helps us model the collisions in our game more reallistically.

To better understand momentum, let's look at an example.

Example 1: Suppose that you are holding a rifle of mass m_R = 3.00 kg loosely in your hands, so as to let it recoil freely when fired. You now fire a bullet of mass m_B = 5.00 g horizontally with a velocity relative to the ground of v_B = 300 m⁄s. We want to know a)the recoil velocity v_R of the riffle, b) The final momentum of the bullet and c) the final momentum of the riffle.

Solution: We are going to consider an idealised model in which the horizontal forces you exert on the rifle are negligible. Then there is no net horizontal force on the system (the bullet and rifle) during the firing of the riffle, and so the total horizontal momentum of the system is the same before and after the rifle is fired (i.e., is conserved).

Take the positive x−axis to be the direction the rifle is aimed. Initially, both the rifle and bullet are at rest, so the initial x−component of total momentum is zero. After the bullet is fired, its x−component of momentum is m_BV_B, and that of the rifle is m_RV_R. Conservation of the x−component of total momentum gives

P_x = 0 = m_BV_B + m_RV_R,

V_R = −(m_B ⁄ m_R)V_B = −(0.00500 kg ⁄ 3.00 kg) (300 m⁄s) = -0.500 m⁄s.

The negative sign means that the recoil is in the direction opposite to that of the bullet. If the butt of a rifle were to hit your shoulder traveling at this speed, you'd feel it. That's what the "kick" of a rifle is all about. It's more comfortable to hold the rifle tightly against your shoulder when you fire it; then m_R is replaced by the sum of your mass and the rifle's mass, and the recoil speed is much less.

The momentum of the bullet is

P_B = m_BV_B = (0.00500 kg)(300 m⁄s) = 1.50 kg · m⁄s.

for the rifle, the momentum is

P_R = m_RV_R = (3.00 kg)(−0.500 m⁄s) = −1.50 kg · m⁄s.

The bullet and the rifle have equal and opposite momenta (the plurar of momentum) after the interaction because they were subjected to equal and opposite interaction forces for the same amount of time.

Notice that the calculations we have performed do not depend on how the rifle is works. In a real rifle, the bullet is propelled forward by an explosive charge; if instead a very stiff spring were used ot give the same bullet velocity, the answers would have been exactly the same.

Well, this is all you need to know about momentum. Try to solve problems were there are collisions between objects.

If you have any queries regarding this tutorial, do not hesitate to contact me.

Best Regards

Fidel