Monthly Archives: February 2016

Where Newton’s Third Law doesn’t work

In the last post, I talked about some of the basics of Newton’s three laws of motion.
Reiterating them.
1. The first law is about a body’s reluctance to change its state of motion – If it’s not acted upon by an external force, a body undergoing uniform motion will moving, and a body at rest will remain at rest.
2. The second law is about how a body reacts to a force – The rate of change of momentum of a body is proportional to the force acting on it.
3. The third law states that for every action, there is an equal and opposite reaction.
Here’s an instance, however, where the third law does not apply.
For this bit, you’ll need a little bit of background in electromagnetism.
A moving charge creates a magnetic field around it. The direction of the field is given by the right hand rule. If the thumb of your right hand points along the velocity of a positive charge, your fingers curl along the direction of the field.
Right hand rule
A charge moving in a magnetic field experiences a force that is proportional to the charge of the particle, its velocity, and the magnetic field.
F = qv x B.
The direction of the force experienced by the particle can be given by Fleming’s Left Hand Rule, depicted below. If your forefinger points along the direction of the field a positively charged particle is moving through, and your middle finger in the direction of motion , your thumb points along the direction of the force experienced by the charged particle.
Fleming's left hand rule
Now look at this figure where two positive charges are moving in directions perpendicular to each other.

2016-02-20 06_54_02

The red charged particle (Particle 1) is producing a field B1. The blue particle (Particle 2) is moving through the field upwards. As it does so, it experiences F21, which pushes it to the right side, as shown by the red arrow.

According to Newton’s third law, Particle 1 should also feel a magnetic force F12 to the left, created by Particle 2. However, since the field produced by Particle 2 (B2) is zero at point 1, Particle 1 feels no force acting on it when it is directly underneath Particle 2.

So, F12 = 0.

Newton’s Third Law does not apply.

If you want to dig deeper and understand why momentum is still being conserved in this scenario, you can mull over reference 3. It’s explored there in great detail.

[Note: I am omitting the Coulomb forces the particles are exerting on each other. They are equal and opposite. It’s the magnetic forces that aren’t obeying Newton’s Third Law.]


  1. Fig1:
  2. Fig2:


Newton’s Three Laws of Motion – A fun exercise

Let me start with an update on my PhD status. Obvious from the frequency of my blog posts, I have been extremely busy with my projects and coursework. But I am glad to say that, thanks to group mates I can trust and talented lab partners I can rely on when I’m in trouble, things could not have been more productive. And honestly, I don’t mind being under a lot of pressure as long as I am being productive.
Okay, now for the topic of this post. I have been wanting for a long time to write about something that’s very basic in physics – Newton’s Laws.
Before I go into detail, here’s a simple question you can ask your friends. And try to answer it as fast as possible, like, in under ten seconds. Come on, you are a smart guy! You shouldn’t take any more time than that.
While you are asking the question, make sure you contract your arm, and make a throwing motion, providing a visual aid for the innocent victim. If you are lucky, you’ll probably make them give you a wrong answer.
It seems like an easy enough question, but you would be surprised how many get this wrong. Of course, the question lacks a lot of detail. Where in space is the object? How far are the nearest bodies that might exert a force on the object?
The object is not going to slow down. Everyone gets this bit right. There’s no air resistance. So nothing slows the ball down. [Unless your time scale is over millennia and the ball loses its momentum bumping into tiny space particles floating around].
Now, why does the ball not speed up? You did exert a force on it that caused it to accelerate, and as I have established before, there’s nothing there to slow it down, right?
Well, it did accelerate as long as your hand was pushing it forward. But as soon as the ball left your hand, it did not have any force pushing on it anymore. So, it would move in a straight line in a constant speed.
But what about the third law? For every action there is an equal and opposite reaction. So if there is a reaction force, why don’t the two forces cancel each other out and the ball remain at rest?
That’s because the action and the reaction force don’t act on the same body. The reaction force exerted by the ball acted on your hand, and decelerated it, as your biceps tied to pull your hand forward. Since the force by the ball was decelerating your hand, it could not cancel out the force your hand was exerting on the ball.
Sweet. So far we’ve covered high school level physics. But honestly, I have seen Olympiad competitors, engineering students, and even PhD students mess up this simple question. Just needs a little misdirection.
Now, after we have kind of established Newton’s laws and their ‘infallibility’, in my next post, I am going to give you an example where Newton’s third law does not seem to work.