# Newton’s Laws of Motion

Did you know that when you throw a baseball in the air or you bounce a basketball on the court, you can use Newton’s laws of motion to explain the motion of the baseball or basketball? In fact, almost all kinds of motions in the world can be explained by these laws.

If you’re going to study physics this year, you’ll soon come to know his three laws of motion very well.

**Sir Isaac Newton**

One of the greatest scientists and mathematicians, Sir Isaac Newton was born in England on December 25, 1643. Did you know that he was born the same year that Galileo died and lived for 85 years?

Isaac Newton grew up with his grandmother and attended Free Grammar School. He eventually went on to study at the Trinity College Cambridge. Newton worked really hard during his college years. When he was at college, he developed a keen interest in math, physics, and astronomy. He managed to receive both a bachelors and master’s degree.

Newton had a habit of writing his ideas in a journal since his young days. Amongst those ideas were also the concepts of motion, which he later called his three laws of motion. He also had worked on topics like gravity, the diffraction of light, and forces. Newton’s ideas were brilliant and so Queen Anne knighted him in 1705. His accomplishments also created the foundations for modern science and revolutionized the world. Sir Isaac Newton died in 1727.

**Motion**

In everyday life, we can see many physical interactions constantly happening all around us like a tree leaf or a ball falling to the ground, a moving car, etc. In fact, everything in the universe is constantly moving. It can either be a marginal movement or a swift one but the movement is always taking place. This change in the position of an object is called Motion.

An object will continue to move in its motion at a constant velocity until and unless an outside force exerts its influence upon the object. The term ‘velocity’ refers both to the speed and the direction in which an object is moving. You can easily recognize an object in motion and an object at rest. When the object does not change its position with respect to the surroundings, the object is said to be at rest.

**What is Motion?**

Motion is the process of an object moving or changing place, or even just changing position.

Some examples of motion are a ball rolling on the ground, an eagle flying in the sky, the motion of the earth around the sun, a rock rolling down a hill, a person inside a moving vehicle vis-a-vis a person outside the vehicle, etc.

There are a lot of factors involved every time an object moves. There are fewer factors involved if an object moves at the same speed in a straight line. However, most movement involves changing the speed of the movement and changing directions.

**Distance and Displacement**

Displacement is the minimum distance between two points while distance is the actual path covered. While displacement is a vector term, distance is a scalar term. Distance and displacement both have SI unit as the meter.

In the figure above, ** AB+BC** is the distance moved and

**is the displacement.**

*AC*On a round trip, the distance is 2 (*AB+BC*) while the displacement is *AC+CA*=0.

Therefore, the distance is never zero while the displacement in one round trip is zero.

Remember that,

**Speed (S) = Distance moved (d)/ Time taken (t)**

The SI unit for velocity and speed is meter/second (m/s).

**Equations of Motion**

In a uniformly accelerated rectilinear motion, the variable quantities are time, speed, distance covered, and acceleration. Simple relations exist between these quantities. These relations can be expressed in terms of equations called the equations of motion.

There are three equations of motion:

- V = u + at
- S = ut +
^{2} - V
^{2 }= u^{2}+ 2as

Where,

V= Final velocity

U=Initial velocity

A = Acceleration

S = Distance travelled by a body

T = Time taken

**Derivation of Equation of Motion**

**The First Equation of Motion**

Consider a particle moving along a straight line with uniform acceleration ‘a’. At t = 0, let the particle be at A and u be its initial velocity and when t = t, V be its final velocity.

Acceleration = Change in velocity/Time

= v – u /t

at = v – u

v = u + at ……… *the* *first equation of motion*.

**The Second Equation of Motion**

Total distance traveled/ Total time taken

s/t

u+v/2

s/t u+v/2

s/t= u+u+at/2

s**=** (2u+at)t/2 = 2ut+at^{2} /2 = 2ut/2+at^{2 }/2 ………. *the second equation of motion.*

**The Third Equation of Motion**

The first equation of motion is v = u + at.

v – u = at… (1)

Average velocity = s/t … (2)

Average velocity= u+v/2 …. (3)

From equation (2) and (3), we get

u+v/2 = s/t … (4)

By multiplying equation (1) and (4), we get

(v – u) (v + u) = at x 2s/t

(v – u) (v + u) = 2as

We make use of the identity a^{2} – b^{2 }= (a + b) (a – b)

v^{2 }– u^{2}= 2as ……… *the third equation of motion.*

**Types of Motion**

We can divide motion into translational, rotational, and oscillatory motion. Let’s understand each of them in detail.

**Translational Motion**

The motion that results in a change of location is known as Translational motion. This implies that an object can be moving and yet not be going anywhere. For instance, you may get up in the morning and go to school (a change in location) but in the evening you’re back at home and in the very same bed from where you started your day. If you’ve to determine how far you’ve travelled in a day then there could be two answers: either you’ve gone to school and back (5 km each way for a total of 10 km) or you’ve gone nowhere (5km each way for a total of zero km). The first answer invokes translational motion and the second one invokes oscillatory motion.

**Oscillatory Motion**

Oscillatory motion is repetitive and fluctuates between two locations. In the earlier example of going from home to school to home to school, you’re moving, but in the end, you haven’t gone anywhere. The oscillatory motion is seen in pendulums, vibrating strings, and drawers (all that motion and nothing to show for it). In the oscillatory motion, it takes a fixed amount of time for an oscillation to occur. This kind of motion is said to be periodic and the time for one complete oscillation (or one cycle) is called a period. Periodic motion is important in the study of sound, light, and other waves.

**Rotational Motion**

The spinning action of an object leads to rotational motion. The earth is in a constant state of motion but it ends up in the same place. Every twenty-four hours it makes one complete rotation about its axis. The sun does the same thing but in about twenty-four days. So do all the planets, asteroids, and comets; each with their own period.

**The History behind the Laws of Motion**

In the sixteenth century, Copernicus suggested that Earth and other planets orbited the Sun, but his model did not have any elements of physics. It did not state the reason why the planets should orbit the Sun. Galileo was censured by the Catholic Church and also forced to retract his statements and belief in the Copernican model. He then realized that to ultimately win the Copernican model, he needed a physical basis. Galileo, therefore, started to quietly develop the new physics needed to explain the law of planetary motions. Isaac Newton, who was born the year Galileo died, built on the foundation laid by Galileo. The resulting creation? It was Newton’s laws, a grand synthesis that explained motions both on Earth and in the heavens with a unified set of laws for the first time.

Sir Isaac Newton (a.k.a. “The Big Fig”) learned a lot from his famous apple-on-the-head incident. He worked on developing calculus and physics at the same time. During his work, he came up with the three basic ideas that are applied to the physics of most motion (NOT modern physics). These ideas have been tested and verified so many times over the years, that scientists now call them Newton’s Three Laws of Motion.

Newton’s laws are used for everything: when people design airplanes, trains, cars, sports equipment, toys, and many other things that have to do with motion. Many students have trouble understanding Newton’s laws of motion because doesn’t it get a bit hard to understand how the laws work without any examples? Let’s take a look at what these laws mean and their real-life applications.

**Overview of the Three Laws of Motion**

Sir Isaac Newton’s three laws of motion are all about the motion of massive bodies and how they interact. His laws may sound obvious to us today, but more than three centuries ago, they were totally revolutionary.

Newton was one of the most significant scientists of all time and his ideas went on to become the basis for modern physics. He also managed to build upon ideas that were put forth by previous scientists like Galileo and Aristotle. He also studied optics, math, and astronomy, thus invented calculus. But there’s still a debate about that as German mathematician Gottfried Leibniz has also been credited with developing it independently at about the same time.

Newton is widely known for his work in gravity and the motion of planets. Urged on by astronomer Edmond Halley after admitting he had lost his proof of elliptical orbits a few years prior, Newton published his laws in 1687, in his seminal work “Philosophiæ Naturalis Principia Mathematica” (Mathematical Principles of Natural Philosophy) in which he formalized the description of how massive bodies move under the influence of external forces.

While creating his three laws, Newton simplified his treatment of massive bodies by considering them to be mathematical points with no size or rotation. This helped him disregard factors such as friction, temperature, air resistance, material properties, etc., and focus on things that can be described exclusively in terms of mass, length and time. Therefore, the three laws of motion cannot be used to understand the behaviour of large rigid or deformable objects. But in many cases, they provide exact approximations.

Newton’s laws are about the motion of massive bodies in an *inertial reference frame*, which is sometimes also called a *Newtonian reference frame*. But Newton never described such a reference frame. An inertial reference frame can be defined as a 3-dimensional coordinate system that is either stationary or in uniform linear motion, i.e., it is not accelerating or rotating. He eventually established that motion within such an inertial reference frame can be explained by three simple laws.

**The First Law of Motion**

**“Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it.” This law is often called “the law of inertia”.**

**What does this mean?**

Now can you see why it’s hard for students to understand the first law? Aren’t those some complicated words? It simply means that there is a natural tendency of objects to keep on doing what they’re doing. But all objects resist changes in their state of motion. In the absence of an unbalanced force, an object in motion will maintain this state of motion.

The law of inertia was initially discovered by Galileo for horizontal motion on Earth and was later established by René Descartes. Before Galileo made this discovery, it was believed that all horizontal motion needed a direct cause. However, Galileo concluded from his experiments that a body in motion would stay in motion unless a force (such as friction) causes it to come to rest.

*Consider the following example:*

When you keep a glass full of water on a table in your home where there is no air flowing, then what will happen to the water level? It will remain the same right? Yes, that is because there is no external force acting upon it. But what if we insert our finger in the glass or move the table fan nearby? The water in the glass will start shaking and will spill out of the glass, right?

This happens because the water was in a state of rest and it wants to continue to be in the state of rest. Therefore, it will push the excess water outside so that it can return to its original state of rest.

There are many more applications of Newton’s first law of motion. The applications are listed below.

- Blood rushes from your head to your feet when you stop quickly or when you ride on a descending elevator.
- The top part of a hammer can be tightened onto the wooden handle by banging the bottom of the handle against a hard surface.
- A brick can be broken into two pieces by a physics teacher by hitting it with a hammer. (Warning: do not attempt this at home!)
- When we have to remove the stuck ketchup from the bottom of a bottle, we turn it upside down and thrust it downwards at high speeds.
- Headrests are available in cars to avert whiplash injuries during rear-end collisions.
- When you are riding a skateboard or a bicycle, you move forward. But when you hit a curb or rock or any other hard object, your speed gets halted abruptly.

**The Second Law of Motion**

**“Force is equal to the change in momentum (mV) per change in time. For a constant mass, force equals mass times acceleration.” F = ma**

So, *F *= *dp*/*dt*

This results force acting a body *F* is equal to the mass of the body *m* times acceleration of the body *a*.

So, *F* = *ma*

The second law is one of the most important formulas in physics, folks. It says that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum, or its direction, or both.

The idea here is very simple because you may already know how it works in real life. Do you need more energy (force) to move a book or a large screen TV? Surely, you know that you need more energy to move a large screen TV. That’s what the second law of motion means.

*Consider the following example:*

Why do you think it is an easier task to push away a slim person than a fat person? Also, why do you think it is easier to kick or move a football than a bowling ball? The answer lies in Newton’s second law of motion. It’s because a fat person obviously has more mass and hence to make him move, one has to exert a greater force. Similarly, the total mass of a bowling ball is a lot more than that of a football, so to make it move, a greater amount of force is required.

**The Third Law of Motion**

**“For every action, there is an equal and opposite reaction.”**

*F*_{AB }= – *F*_{BA}

Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. This final law is also called the law of action and reaction. It is also a crucial discovery that analyzes problems of static equilibrium, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion. The forces it describes are real ones, not mere bookkeeping devices.

Finally, here’s something without any complicated words. Do you like to go to something like skating? The next time around when you go for a skating trip, try this simple experiment. Keep your skates on, find someone and place your palms against that person’s palms. Then, apply a little force and push off and you will see that both of you are going in opposite directions. This is Newton’s third law of motion in action.

*Consider the following example:*

When a fireman opens the nozzle of the water pipe connected to the fire preventive unit, he usually goes a few steps backward. Why does he do that? It’s because the water that comes out of the water nozzle exerts an equally opposite force towards the water hose, due to which the fire personnel is pushed backward. Did you know even a textbook lying on the floor is an example of this law? If the book exerts a force of approximately 10 Newton on the floor, then the floor also exerts an equally opposite force of 10 Newton onto the book. Amazing, isn’t it?

“Newton’s Laws of Motion” is one of the easiest and important chapters of the school syllabus. These laws are not new to students as the subject keeps coming up even in previous classes. The chapter is important not only because it fetches 2-3 questions in most of the examinations, but also because it is a prerequisite to the other chapters of Mechanics. Know Why Mechanics Cannot Be Learned In a Classroom

The three laws of Newton have been established by innumerable experiments by scientists over the past three centuries. They are still widely used until this day to describe the kinds of objects and the speeds that we encounter in everyday life. These concepts create the foundation of what we now call classical mechanics, which is the study of massive objects that are larger than the very small scales addressed by quantum mechanics and that are moving slower than the very high speeds addressed by relativistic mechanics.

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