Newton and Recoil of a Gun

While preparing for the entrance examination for the Long Gunnery Staff Course (LGSC) in 1988, the prescribed book on basic physics had a question – Recoil of a gun is based on which of Newton’s Laws of Motion?  The options were:-

  • First Law
  • Second Law
  • Third Law
  • None of the above.

Based on my previous knowledge, I presumed that the answer is the Third Law, but the book stated that it is the Second Law.  I sought help of our senior officers who had graduated from LGSC and they all said that it’s the Third Law.  I concluded then that it might be a typo error in the book.

In 1996, I attended Technical Staff Course.  Those of us without any technical qualifications like B Tech had a six months scientific orientation course prior to the commencement of the course.  This orientation course covered basic sciences and mathematics. 

During the class on Newton’s Laws of Motion by Dr Ganesh, a young scientist, I queried about Newton’s Laws and Gun’s Recoil to clear my mind of the lingering doubt.  Dr Ganesh explained it in detail.

  • The gun with the bullet/ shell housed inside prior to pressing of the trigger, total momentum of the system equals zero. 
  • On pressing the trigger, the bullet gains velocity and the gun recoils.  Here too the total momentum of the system does not change.  Momentum is the product of the Mass and Velocity. 
  • That is why we calculate recoil by equating the momentum of the Gun and the bullet by the formula – Mg X vg = mb x Vb where
    • Mg is Mass of the Gun
    • vg is Velocity of the Gun
    • mb is Mass of the Bullet
    • vB is Velocity of the Bullet

We account for both the forward momentum of the bullet and the rearward momentum of the gun.  Here the sum of the magnitude and direction of the momentum of both the bodies involved does not change being in opposite direction. Hence, momentum of the system is conserved.

This conservation of momentum is why gun recoil occurs in the opposite direction of bullet projection – the mass times velocity of the projectile in the positive direction equals the mass times velocity of the gun in the negative direction. Thus the sum of momentum before the trigger is pulled or when the gun fires remains the same.

Thus, the recoil of a gun is attributed to the Law of Conservation of Momentum – that is the Second Law.

Now I realised that the basic Physics book I read while preparing for LGSC was correct.