Newton's Third Law of Motion

Momentum and Recoil

We are all familiar with guns recoiling when fired. We may not have fired a gun ourselves but we have watched enough movies to see this phenomenon in action. Newton's Third Law of Motion states that "Every action has an equal and opposite reaction". What Newton was talking about is conserving momentum. We can also state the Law of Conservation of Momentum. This law states that, "In the absence of an external force, the momentum of a system remains unchanged". Now we have introduced two new words, system and momentum. Let's clarify these two terms.

What is momentum? It is a quantity much like force and velocity which have magnitude and a direction.
We express the momentum of an object by the formula below

Momentum = velocity X mass of the object

We can see from the formula that an elephant travelling at 3 m/s has a greater momentum than a mouse travelling at 3 m/s. A truck travelling at 100 km/hr has more momentum than when it travels at 30 km/hr. A stationary object has no momentum.

What is a system? A system is a collection of two or more objects that interact with each other. For example, a cannon and a cannon ball form a system, as does a rocket in the barrel of a rocket launcher. Two colliding billiard balls also form a system.
Now, the Law of Conservation of Momentum states that the momentum of a system must be conserved. OK! so when I fire a bullet from a gun the total momentum of the gun and the bullet, known as the system, should be equal to the momentum of the gun and bullet before firing. As the bullet leaves the gun barrel it has a momentum equal to its velocity multiplied by its mass (momentum=velocity X mass). The gun must now move in the opposite direction with a certain velocity so that its momentum is exactly equal in magnitude and opposite in direction to the bullet's momentum. This is why the gun recoils. The bullet is not as heavy as the gun but escapes from the barrel at speeds around 860 m/s. The gun is much heavier than the bullet so it recoils at speeds significantly less than that of the bullet but enough to give a serious jolt.
A recoilless gun also obeys the Law of Conservation of Momentum. The gun does not recoil because it vents gas out the back. The momentum of the gas escaping out the rear of the gun is equal to the momentum of the shell. The gun therefore does not have to move backwards so that momentum is conserved.
As seen on the right, the mass and velocity of the gas escaping from the rear of the gun is equal to the velocity and mass of the shell escaping in the forward direction. Otherwise the gun would recoil violently



Recoilless weapons have been used successfully since WW2. They are generally used to fire heavier, self-propelled shells that can engage tanks and heavy armour.


A 200 kg canon recoils with a speed of 0.4 m/s. With what speed does the 5.2 kg cannon ball exit the barrel of the cannon?


When the guns of a battle ship fire the ship shows no signs of being pushed in the opposite direction. Why?


Explain why this gun does not recoil backwards as the cannon above did.


A 32.0 kg cannon ball is fired with a speed of 80 m/s. The cannon moves in the opposite direction with a speed of 2.0 m/s. Assuming there is no friction, what is the mass of the cannon?