First Law of Motion

An object that is at rest will remain at rest unless a nonzero net (or total) force is exerted on it. This one is fairly easy to believe and sounds intuitive enough. However, the next part of the first law might sound less plausible. Simply stated, an object moving at a constant velocity will continue to move at a constant velocity (moving at a constant speed and in a straight line) unless a nonzero net (or total) force acts upon the object. Recall that constant velocity means that the object is moving at a constant speed and in a constant direction.

    At this point, you might be thinking to yourself about something you saw in the world that contradicts the statement I just made. For instance, think of a car rolling in a straight line while in neutral. If what I stated above were true, then the car should be able to roll in a straight line at a constant speed forever. This is obviously not true in real life because everyone knows the car eventually comes to a stop. This certainly seems to prove that Newton's first law of motion is false. Or does it? I assert that the above observation is consistent with Newton's first law which states that an object moving at a constant velocity will continue moving in that fashion unless a nonzero net force acts upon that object. You might already know the answer.

    It is true that the car would continue to move in a straight line at a constant speed if there was no net force acting on the car. However, is there really no net force acting on the car? In fact, there is a nonzero net force acting on the car, causing it to slow down. And, you probably already know what that force is. The force responsible for slowing down the car is friction. Therefore, the above observation about a car slowing down while in neutral is not inconsistent with Newton's first law of motion. It just seems to contradict it at first. If this is confusing, pause for a moment and think about it for awhile.

    This is a pretty surprising fact to most people when they first hear it. If we were able to remove all the friction between the ground and a ball, once you start the ball rolling, it would roll on forever in a straight line.

    This is a perfect tie-in to Newton's second law. We just discovered that objects like to move in straight lines and at constant speeds unless a force acts upon them. In fact, when a force acts on an object, the force causes the object to change its velocity. In other words, forces cause objects to accelerate.

Second Law of Motion

Simply stated, a force causes an object to accelerate. Whenever you see an object accelerating, there must be an external force acting on the object because, as stated in Newton's first law, objects move at a constant velocity unless acted upon by an outside force.

    Mathematically, Newton's second law of motion can be expressed by the following formula: a = F/m where a = acceleration, F = force, and m = mass.

    What this formula tells us is that force causes an object to accelerate. However, it also tells us that the acceleration an object feels, in response to an applied force, does not solely depend on the amount of force applied. It also depends on the mass or inertia of that object. It also tells us that the more mass an object has, the less it accelerates in response to an applied force. This makes intuitive sense. For instance, if I apply the same force to a cotton ball and an elephant, the cotton ball would experience a greater acceleration than the elephant because the elephant has much more mass or inertia. Therefore, an object with a greater mass has a better tendency to resist a change in its motion when an external force is applied to that object. In other words, we say that the elephant has more inertia than the cotton ball.

    Part of the beauty of math is that all this can be elicited from looking at the formula above in a much more compact form without reading an entire paragraph of explanation.

    Newton's third law states that whenever a force is exerted, an equal and opposite force arises in reaction to this force. In other words, every force has an equal and opposite reaction force.

For example, when you push on a wall, the wall will also push back on you with an equal and opposite force. By the way, the "Newtons" in the figure above is the unit in which force is measured. In what follows, I will write "N" in place of "Newtons". For example, 5 Newtons of force will be written as 5 N.

    Some of you might be wondering why you don't move backwards even though the wall is pushing you backwards. How very astute. The reason why you don't move backwards when you push against a wall is because static friction is pushing you back with an equal amount of force to the right so that you don't move anywhere. In the above example, static friction would be pushing the person to the right with 5 N of force, so that the person would experience zero total (or net) force, hence the person does not move.

    This brings up an important point, i.e., that forces add up. We will come back to this point later when we discuss force in more detail.

    So, if Newton's third law is true, and the wall pushes back on us just as hard as we push back on it, there must be some way of seeing that in the real world. Well, there certainly is. If you have ever gone ice skating or in-line skating (notice I'm not using the word Rollerblading) or roller skating (if you are really old), you can probably recall the example to follow.

    Recall that the only reason why you didn't move when you pushed against the wall was because there was friction pushing you back to the right. Well, if you go skating, ice skating for example, you are reducing the friction between you and the floor because ice is very slippery. As a result, there isn't enough friction to compensate for the wall pushing you back. If you push against the wall while ice skating, you will move backwards as a result of the reaction force to you pushing against the wall.