Newton’s Laws of Motion are the fundamental laws of Physics I. He originally wrote these laws in Philosophiae Naturalis Principia Mathematica, more commonly known today as the Principia.
The three laws can be stated in words as:
An object at rest will remain at rest, and an object in motion will continue in motion with a constant velocity, unless acted upon by a net external force.
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Forces come in pairs which are of the same magnitude but opposite direction.
or mathematically as:
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Newton’s cradle operates on the principles stated in his three laws.
9.2 Newton’s First Law
The First Law is often referred to as the law of inertia. Inertia decribes an object’s resistance toward a change in its motion. Thus, the main concept of the first law is that objects tend to retain their motion unless a net force causes that motion to change. If the net force on an object is zero, its motion will not change. So, an object at rest will remain at rest. An object in motion will continue in motion with constant velocity. In other words, there is no acceleration when the net force is zero.
9.3 Newton’s Second Law
The Second Law is the lifeblood of physics. Any net force will result in the acceleration of an object. You will note that the first law is just a special case of this one. The formula given above is simple and easy to follow. Unfortunately, there is a caveat in that this formula does not account for the possibility that mass might vary as a function of time. This is not necessary for a Physics I course. However, this is no longer trivial when studying rocket propulsion as the mass of a rocket does indeed vary with time.
9.4 Newton’s Third Law
The Third Law is quoted least often but is important nonetheless. It states that forces always come in pairs. Two objects, A and B, will always exert equal and opposite forces on one another. If A is your left hand and B is your right hand, this law states that, if you push you hands together, neither one will be able to push harder against the other (no matter how you push). The same force that you exert on one will be returned to the other in equal magnitude and opposite direction. This is not intuitive nor is it trivial. Another commonly used statement for the third law is that forces come in pairs.
Chapter Summary
These laws are extremely useful when drawing free-body diagrams. If an object is at rest, the forces must be balanced. If an object is moving with constant velocity, the forces must also be balanced. Finally, if an object is accelerating (positively or negatively), then it must have a net force not equal to zero.
By committing Newton’s Three Laws to memory, you expand your physics toolbox immensely. However, at the very least, you must memorize the second law: One of the most useful problem-solving techniques is to just write this law down and see where it takes you. Many times, this law is the key to finding the solution to your problem.
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Knowledge Check
Answer the quiz questions below.
What does Newton’s First Law of Motion describe?
It describes the relationship between force and acceleration.
Incorrect. Newton’s first law, also known as the law of inertia, describes the tendency of an object to retain its motion unless acted upon by a net external force.
It describes the equality of action and reaction forces.
No, that’s Newton’s third law. The first law, also known as the law of inertia, talks about the persistence of an object to maintain its state of motion until acted upon by a net external force.
It describes an object’s resistance to change its motion unless acted upon by a net external force.
Correct! Newton’s First Law, also known as the Law of Inertia, tells us that an object at rest will stay at rest and an object in motion will stay in motion with the same speed and direction unless acted upon by a net external force.
What is the key concept in Newton’s Second Law of Motion?
Objects at rest will remain at rest unless acted upon by a net external force.
Incorrect, that’s Newton’s first law. Newton’s second law describes the relationship between an object’s mass, its acceleration, and the applied force.
Every action has an equal and opposite reaction.
No, that’s Newton’s third law. The second law tells us that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
Exactly right! Newton’s Second Law of Motion defines the relationship between acceleration, force, and mass. The more force that’s applied to an object, the more it accelerates, but the more mass an object has, the less it accelerates for a given force.
How can Newton’s Third Law of Motion be best described?
An object at rest will remain at rest, and an object in motion will stay in motion, unless acted upon by a net external force.
No, that’s Newton’s first law. The third law states that for every action, there is an equal and opposite reaction.
The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
No, that’s Newton’s second law. The third law says that for every action, there is an equal and opposite reaction.
For every action, there is an equal and opposite reaction.
Correct! Newton’s Third Law of Motion tells us that forces always come in pairs. When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first.
An object is moving with a constant velocity. According to Newton’s laws, what can we conclude?
There is no force acting on the object.
Not quite. It’s not that there are no forces acting on the object, but rather that the net force acting on the object is zero. This means that the forces are balanced and result in no change in velocity, hence a constant velocity.
The object is experiencing a net force.
No, if an object is moving with a constant velocity, the net force on it is zero. This is because there is no acceleration (change in velocity), so the forces acting on the object must be balanced.
The net force acting on the object is zero.
That’s right! If an object is moving with a constant velocity, it means that the net force acting on it is zero. This is a direct application of Newton’s First Law of Motion.
If a car is accelerating, what can we infer from Newton’s Second Law?
The car is experiencing no forces.
Incorrect. If a car is accelerating, it must be experiencing a net force. According to Newton’s Second Law, an object’s acceleration is directly proportional to the net force acting on it.
The forces acting on the car are balanced.
No, if the forces were balanced, the car would be moving with constant velocity (which could be zero), not accelerating. When a car is accelerating, there must be a net force acting on it.
There is a net force acting on the car.
That’s correct! According to Newton’s Second Law, an object will accelerate if and only if there is a net force acting on it. So, if a car is accelerating, it must be experiencing a net force.
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One of the most useful problem-solving techniques is to just write this law down and see where it takes you. Many times, this law is the key to finding the solution to your problem.
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