Understanding Newton’s Laws of Motion

FROM THE LECTURE SERIES: THE JOY OF SCIENCE

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

Isaac Newton trod a different path from the earlier scholars and classified physical motion into two categories. This distinction between uniform motion and acceleration was a great insight that formed the basis of Newton’s three laws of motion. How did these assumptions provide an entirely different perspective to scientific understanding during his times? 

Representation of Newton's second law of motion.
Newton’s second law of motion defines the relationship between force, mass, and acceleration. (Image: BrainCityArts/Shutterstock)

Different Types of Motion

Isaac Newton classified physical motion into two different categories—uniform and non-uniform motion. This helped him formulate the three laws of motion. Newton considered both an object moving in a straight line at a constant speed and, as a special case, an object at rest as uniform motion.

Newton categorized all other imaginable motion, including that of planets moving in their circular orbits, as non-uniform motion or acceleration.

Newton differed from the earlier belief that planets moving in a perfect circular motion at constant speed were in uniform motion. He defined any change in speed and direction as acceleration and therefore argued that orbital motion is a kind of acceleration.

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

Mathematical Treatment of Acceleration

Newton’s definition of acceleration describes both positive and negative acceleration. While speeding up is referred to as positive acceleration, an action of slowing down, such as applying the brakes of a car, is negative acceleration. 

Mathematically, acceleration is expressed using the concept of the vector. In a mathematical vector, both direction and speed are defined. It can be represented as an arrow, where the arrow denotes the direction, and the length corresponds to the speed.

Learn more about the nature of energy.

Newton’s First Law of Motion

Every body continues in its state of rest or of uniform motion in a [straight] line unless it is compelled to change that state by forces impressed upon it.

This means an object will not change its motion unless acted upon by an external force. This law conveys three distinct types of behavior by objects. The first one being that an object moves at a constant speed in the same direction as it goes along. However, this situation is practically impossible in real life as there are forces acting around it all the time.

A diagram of an aeroplane to illustrate Newton’s first law of motion.
Newton emphasizes that if an object accelerates, then there is a force involved. (Image: Fouad A. Saad/Shutterstock)

Another type of behavior is when an object is at rest and continues being at rest without disturbance to both its velocity or direction. This is the special case where the vector is just a point.

And finally, the third and most common type of behavior is when an object accelerates under the influence of a force. Though Newton does not specify the type of force in his first law of motion, he emphasizes that if an object accelerates, then there is a force involved. Thus, Newton’s first law provides an operational definition of force.

Learn more about universal gravitation.

Newton’s Second Law of Motion

The acceleration produced on a body by a force is proportional to the magnitude of the force and inversely proportional to the mass of the object.

In other words, when the force acting on the object is higher, the acceleration is also higher, but when the mass of an object is increased or higher, the acceleration decreases. Therefore, the more massive the object the greater the force that needs to be applied.

The second law defines the mathematical relationship between three measurable quantities. It can be expressed as force equals mass times acceleration. The unit of measurement is called a ‘newton’, which can be defined as the force required to accelerate a one-kilogram mass by one meter per second per second (m/s2).

Applications of the Second Law of Motion in Everyday Life

The power of mathematics in quantifying the natural world is incredible. These mathematical equations in conjunction with science help to solve many day-to-day problems. The incredibly simple equation of Newton’s second law of motion helps to solve real-life problems such as constructing stable bridges and buildings or calculating the force required to toss a satellite into its orbit.

Learn more about the ordered universe.

For every action there is an equal and opposite reaction.

A diagram of a balloon to illustrate Newton's third law of motion.
In his third law of motion, Isaac Newton suggests that forces always act simultaneously in pairs. (Image: Fouad A. Saad/Shutterstock)

With this simple yet subtle law, Newton suggests that forces always act simultaneously in pairs. And these forces are equal and opposite.

For instance, when a force is applied to throw a ball, the ball also exerts a force on the hand as the action of throwing is performed.

Similarly, if a car crashes into a tree, the tree exerts the same amount of force on the car as the car on the tree, but the damage is to both of them. In both these examples, the simultaneity of forces acting in pairs is obvious.

Common Questions about Understanding Newton’s Laws of Motion

Q: What are some examples of using Newton’s second law of motion in day-to-day life?

Newton’s second law of motion helps to solve real-life problems such as constructing stable bridges and buildings or calculating the force required to toss a satellite into its orbit.

Q: How did Newton classify the different types of motion?

Newton classified physical motion into two different categories—uniform and non-uniform motion. Uniform motion happens when an object moves in a straight line at a constant speed or when an object is at rest. All other motion is classified as non-uniform motion or acceleration.

Q: How does Newton describe acceleration?

Newton states that if an object accelerates, then there is a force involved. Newton describes acceleration as both positive and negative. Speeding up is referred to as positive acceleration, and the action of slowing down, such as applying the brakes of a car, is referred to as negative acceleration. 

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