Newton’s Third Law of Motion and the Concept of Momentum

FROM THE LECTURE SERIES: THE JOY OF SCIENCE

By Robert M. Hazen, Ph.D., George Mason University

The equal and opposite forces of the subtle third law of motion led to the new concept of the law of conservation of momentum. Isaac Newton formulated a set of mathematical laws to predict the motion of objects anywhere in the universe. How did the concept of momentum and the laws of conservation help in understanding the different aspects of the physical universe?

Image of Newton's Cradle - a series of swinging spheres.
Newton’s cradle, a series of swinging spheres, demonstrates the concept of conservation of momentum and energy. (Image: Nathapol Kongseang/Shutterstock)

Isaac Newton analyzed the motion of orbiting objects, a very different approach from that of his contemporaries. According to Newton’s third law of motion, forces act in pairs. For instance, if someone swings a ball around their head, they are exerting a force to hold the ball in place. At the same time, the ball is also exerting a force away from them and these forces are equal and opposite. The former is called centripetal acceleration and the latter is called centrifugal acceleration. 

Learn more about the nature of energy.

The Subtle Third Law of Motion

A diagram using a balloon and the Earth to illustrate the third law of motion.
In the third law of motion, forces always act in pairs. (Image: Designua/Shutterstock)

Newton’s third law of motion manifests itself in subtle ways. For instance, the recoil of a rifle causes an explosion that creates a cloud of gas. While the gas pushes the bullet forward, the bullet pushes the gas. The gas pushes the rifle but the rifle pushes back on the gas. The gun pushes the shoulder of the gunman, but his shoulder pushes the gun.

And despite the relatively larger size of the rifle in comparison to the bullet, the bullet accelerates to a higher velocity. All these are equal and opposite forces that occur more or less simultaneously.

The launching of a rocket is another consequence of equal and opposite forces. While the rocket is being pushed by the expanding gases, it accelerates faster and faster, the gases on the other hand though being pushed by the rocket aren’t physically connected to each other and diffuse outward.

Thus, a rocket can be accelerated by applying a constant force on it. This example also demonstrates that a small but steady force acting over a long period of time could accelerate an object to very high velocities.

This is a transcript from the video series The Joy of Science. Watch it now, on The Great Courses Plus.

The Concept of Momentum

The concept of momentum is a consequence of Newton’s third law of motion. When two objects collide, the objects bumping into each other exert equal and opposite forces on each other. Each of these objects senses unbalanced forces acting on them but the entire system feels no force at all.

According to Newton’s law of motion, the total momentum experienced by the object depends on the force acting on it. The momentum remains unchanged in the absence of external forces. 

An important idea of Newtonian mechanics is that when two objects collide, the total momentum remains exactly the same before and after the collision. Mathematically, momentum can be defined as the product of the mass of an object and its velocity. The sum of mass times velocity before and after the collision must be equal.

Learn more about universal gravitation.

Laws of Conservation

When the property of an object remains unchanged, it is said to be conserved. Certain physical quantities do not change for a closed system and these are reflected in aspects of the physical universe as the conservation of angular momentum and momentum, the conservation of mass, and the conservation of energy. These conservation laws provide symmetry and an underlying sense of beauty to the universe.

Learn more about celestial and terrestrial mechanics.

The Law of Conservation of Angular Momentum

The law of the conservation of angular momentum states that when no external force acts on an object, no change will occur in angular momentum. This means that an object which rotates will continue to rotate until it is acted upon by a force. A spinning top is a classic example of conservation of angular momentum, where it will continue to spin unless friction slows it down.

A small spinning top held on someone's hand.
A spinning top is an example of conservation of angular momentum. (Image: Rashman/Shutterstock)

The Earth is a large spinning top that rotates on its axis once in twenty-four hours. But over millions of years, the Earth’s rotation has slowed down by the Moon’s gravitational pull. However, since the angular momentum of the Earth–Moon system has to be conserved, the angular momentum of the Moon has increased over the years.

As a result, the Moon spins slightly faster and the orbit of the Moon has moved farther away from the Earth. These examples illustrate that we live in an amazing interactive system—all of which can be analyzed by Newton’s laws of motion.

To summarize, Sir Isaac Newton made critical advances in understanding the laws of motion. Newton’s three laws of motion together provide a complete framework for investigating and understanding all the forces of motion that occur in our lives and the universe.

Common Questions about Understanding Newton’s Laws of Motion

Q: What is Newton’s third law of motion?

According to Newton’s third law of motion, forces act in pairs, and these forces are equal and opposite. For example, when two objects collide, the objects bumping into each other exert equal and opposite forces on each other.

Q: What are the forces of centripetal and centrifugal acceleration?

A ball that is swung around someone’s head demonstrates the forces of centripetal and centrifugal acceleration. The force that is exerted to hold the ball in place is the centripetal acceleration. At the same time, the force that the ball is exerting away from them is called centrifugal acceleration. 

Q: What is an example of the law of the conservation of angular momentum?

The law of the conservation of angular momentum states that when no external force acts on an object, no change will occur in angular momentum. An example of this is a spinning top, where it will continue to spin unless friction slows it down.

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