A bullet being fired from a gun

Section 1: Conservation of Momentum in Firearms

Understand the principle that momentum is conserved during a gun firing. That is, the total momentum before and after the firearm discharges is the same.
When a bullet is fired, the momentum of the bullet moving forward is equal and opposite to the momentum of the gun recoiling backward. This is an application of Newton’s third law of motion.
Bear in mind that even though the firearm and bullet have equal momentum, the bullet has much higher velocity due to its lower mass according to the formula momentum = mass x velocity.

Section 2: Energy Transfer in Firearms

Grasp that energy is transferred from the firearm to the bullet when the gun is fired. The stored chemical energy in the gunpowder is converted into kinetic energy in the bullet and gun, as well as thermal energy and sound energy.
Understand that the kinetic energy of the moving bullet and recoiling gun is described by the formula 1/2 m v^2, where m is the mass and v is the velocity.
Appreciate that not all the energy is efficiently transferred to the bullet’s kinetic energy - some is wasted in the form of heat, vibration and sound.

Section 3: Impulse and the Firing Process

Familiarise yourself with the concept of impulse, which is the change in momentum of an object when a force is applied over a time period.
Recognise that the discharge of a firearm involves a large impulse, because a large force is applied over a short time, causing the bullet’s velocity and thus momentum to change rapidly.
Remember the formula for impulse is force x time and its unit is the newton-second (N.s) which is equivalent to kilogram metre per second (kgm/s).

Section 4: Understanding Recoil

Realise that the recoil of the firearm is an application of Newton’s third law of motion: for every action, there is an equal and opposite reaction.
Know that the backward momentum of the firearm (recoil) is equal to the forward momentum of the bullet.
Understand that although the momentum is the same, the recoil velocity of the gun is much lower than the bullet’s velocity due to its larger mass.
Draw upon your understanding of vectors to handle scenarios in which both the bullet and the gun aren’t moving along a straight line.

Make sure to practise applying these principles to solve numerical problems using the appropriate formulas and units, and revisit the topic of vectors as necessary to confidently handle 2D and 3D problems.