Newton's Laws

Newton's Laws

Newton's three laws of motion tell us how a body moves under different conditions. They are:

A body will remain at rest, or at a constant velocity, unless acted on by a resultant force.
The rate of change of the momentum of a body is directly proportional to the resultant force acting on it.
For every action on a body, there is an equal and opposite reaction on another body.

If you compare my version above, with what you would read in most physics textbooks, you would find a slight difference in the words I used. What I have done is to make the meaning of each law more explicit. As I shall explain, the laws are already abstract enough, and any clarification should help in the understanding.

Exactly how abstract are they? Look at the first law. If there is no external force, a body can be at rest. The sounds simple enough. How can it move at constant velocity if there is no external force? Surely, friction would cause it to slow down and stop? This is what a new student would often think. The reason is that if friction is the only force acting on the body, then friction is the resultant force. Since this resultant force is present, the body would neither be at rest, nor at constant velocity. In this case, it is slowling down!

A related example on the first law that could be confusing, is that of pushing a body. A new student may think that a force has to be applied if the body is to remain at constant velocity. In fact, this is only true if there is friction. If we imagine a perfectly smooth floor, then the body could move at a constant velocity on its own, until it hits something.

In the second law, momentum means mass times velocity. For example, the law means that the rate of change of velocity, i.e. the acceleration, is proportional to the resultant force. This is clear enough. It also means that the direction of the acceleration must be the same as the direction of the force, because both are vectors and so both have directions. This is less obvious.

There is also the meaning of the word "resultant." If there are two forces, say 10 N to the right and 2 N to the left, then the resultant is 8 N to the right. That is, it is the combined effect of all the forces acting on the body. So if I push a body on the floor with a force of 10 N, I must remember to subtract the frictional force if I need the resultant force.

Law three is perhaps the most confusing. Many students, old and new, would think that if there is always an equal and opposite reaction, then the resultant force on a body is zero, and it must remain at rest. When a ball hits a stone, the stone pushes back the the ball. If the force from the ball on the stone is the action, then the force from the stone on the ball is the reaction. Notice that the action is on the stone, and the reaction is on the ball. So the two forces at on different bodies! So there is no way they can cancel each other.

Another confusing situation is when a person pushes something away. If you push your book on the table away from you, then the third law says that the book would push back at you. Surely this cannot happen if the book is moving away? Actually, a body that is moving away can still push back at you. We know this because if it does not push back at you, then you would not feel that your hand is pressing on the book when you push it. You should feel nothing at all! The fact the the book is resisting your hand, and you cannot push it as fast as if there is nothing in front, which means that it is pushing back at you.

Thus, we see that the few words used in each law must be understood carefully, and can be applied to many different situations. In this sense, they are very abstract. We can only understand them by learning many different examples.

The Physics Notes