What is the Newton’s Law of Motion?

Newton’s law of motion can be best defined as the law which explains the motion and rest position of a body and the force acting on it, Newton was the first scientist who explains the law of motion in a very perfect manner. In this topic, we will discuss all the details of these laws of motion.

Who was Newton in the history of Sciences?

Sir Isaac Newton FRS was an English mathematician, physicist, astronomer, alchemist, theologian, and author who was known in his time as a “natural philosopher.” He was born on December 25, 1642, and died on March 20, 1727. He was an important part of the Enlightenment, which was a change in the way people thought about things. His book, Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), was first published in 1687. Newton also made important contributions to optics, and he and Gottfried Wilhelm Leibniz, a German mathematician, are both credited with creating infinitesimal calculus.

In the Principia, Newton wrote about the laws of motion and universal gravitation. These were the most widely accepted scientific ideas for hundreds of years until the theory of relativity came along. Newton used his mathematical description of gravity to come up with Kepler’s laws of planetary motion. He also used these laws to explain tides, the paths of comets, the precession of the equinoxes, and other things.

This proved that the Sun is at the center of the Solar System, putting to rest any doubts about the Sun’s position. He showed that the same rules could be used to explain the movement of both things on Earth and things in space. The geodetic measurements of Maupertuis, La Condamine, and others later confirmed Newton’s idea that the Earth is an oblate spheroid. This was enough to convince most European scientists that Newtonian mechanics was better than other systems.

How many Laws of Motion were discovered by Newton?

In the book “Principia Mathematica Philosophiae Naturalis” from 1686, he wrote about his three laws of motion. Newton changed science by coming up with his three laws of motion. The names of these laws were :

• Newton’s 1st Law of Motion
• Newton’s 2nd Law of Motion
• Newton’s 3rd Law of Motion

Newton’s First Law of Motion

Newton’s first law says that an object will stay still or move in a straight line at a constant speed unless it is externally forced by applying any External Force to change its state by an outside force. Newton’s 1st Law of motion is called the Law of Inertia. According to Newton’s 1st Law of motion, the Net Force applied to the body which is at rest or in constant motion will be zero.

Law of Inertia

The word “inertia” comes from the Latin word “iners,” which means “to do nothing” or “to be slow.” The word “inertia” can also mean an object’s resistance to a change in its speed. This includes changes in how fast or which way the object is moving. Newton’s 1st Law of motion is called the “law of inertia” because it says that every physical object has a property that makes it resist changes in its state of motion or rest.

For example:

When a bus makes a sharp turn, people tend to fall out of the bus. It is due to inertia that they want to continue their motion in a straight line and thus fall outwards.

External Force

An external force is a change in an object’s mechanical energy, which can be either its kinetic energy or its potential energy. These forces come from outside sources. Friction, normal force, and air resistance are all examples of forces that come from the outside.

Which situation is contrary to Newton’s First Law of Motion?

There are two things that must be true for the first law of motion to be true:

• When an object is at rest, its velocity (v = 0) and its rate of change of velocity which is acceleration (a = 0) are both 0. Because of this, the object stays still.
• When an object is moving, its velocity is not zero (v ≠ 0), but its acceleration is still zero (a = 0). So, the object will continue to move in the same direction and at the same speed.

Newton’s First Law of Motion by an Example

Case 1:

Take a block and put it on a smooth surface. When we say that something is smooth, we mean that there is no friction on the surface. The block is not moving; it is at rest.

Now, let’s look at what’s pulling on the block. Gravity and the normal reaction of the surface are the only forces acting on the block. It isn’t being pushed or pulled in the horizontal direction. Since the forces in the vertical direction are the same size, they cancel each other out, so there is no outside force acting on the block. Since this block is not moving, it shows that Newton’s first law of motion is true.

Case 2: Now, if we apply a constant horizontal force F to the block, it will start to move with a constant acceleration in the direction of the force.

Example of Newton’s First Law of Motion in Daily Life

Newton’s first law of motion is shown by the fact that we have to wear a seat belt while driving a car. If there’s an accident or the brakes are slammed on quickly, the body will likely keep moving forward, which is probably fatal. Seat belts stop your body from moving forward on its own because of inertia, keeping you out of danger.

Newton’s Second Law of Motion

When a net force acts on a body, the body moves in the same direction as the net force. The magnitude of this acceleration is directly proportional to the net force acting on the body and inversely proportional to its mass. So, The rate of change of momentum is equal to the force. Force is equal to mass times acceleration for a mass that stays the same.

The acceleration of a body is directly related to the total force acting on it and inversely related to its mass. This means that when the force acting on an object gets stronger, the object moves faster. In the same way, an object’s speed slows down as its mass goes up.

Mathematical derivation of Newton’s 2nd Law of motion

The acceleration of an object caused by a net force is directly proportional to the size of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

In the form of an equation, this statement looks like this:

The above equation can be rearranged into a familiar form:

Newton’s second law can be written as Since force is a vector,

The equation shows that the direction of the net force vector and the total acceleration vector is the same.

Derivation of Newton’s 2nd Law of motion for changing mass

Let’s say that a plane is at a point (0, where X₀ is the location and t₀ is the time). The plane weighs m₀ and moves at a speed of v₀. When a force F acts on the plane, it moves to point 1, which is defined by the location X₁ and the time t₁. During the flight, the plane’s weight and speed changed to m₁ and v₁. If we know how much force is acting, Newton’s second law tells us what the new values of m₁ and v₁ are.

Taking the difference between point 1 and point 0, we get the following equation for the force acting on the plane:

Let’s say the mass stays the same. This is a good assumption for an airplane because the only change in mass between point “1” and point “0” would be the fuel burned. If we only look at small changes over time, the weight of the fuel might not be that big compared to the rest of the plane. When we talk about the flight of a bottle rocket, on the other hand, the mass doesn’t stay the same, so we can only look at how the momentum changes.

Derivation of Newton’s 2nd Law of motion for constant mass

Newton’s second law can be summed up like this for a mass that stays the same:

We know that the change in speed divided by the change in time is the definition of acceleration.
The second law then comes down to a form that is easier to understand:

The above equation tells us that if an object is hit by a force from the outside, it will speed up. The amount of force is directly related to how fast something is moving and inversely related to how heavy it is.

SI unit of Newton’s 2nd Law of Motion

The SI unit of Force is Newton (N), so according to Newton’s 2nd law of motion when 1 Newton Force is applied on the body whose mass is 1Kg, it will accelerate 1ms^-2 in the direction of applied force.

The force of one Newton can also be expressed as:

1N =1Kg * 1ms^-2

Newton’s Second Law Examples and Applications

• Riding a Bicycle
  When we ride a bike, we put force on the pedal, which makes the bike move forward at a certain speed. The person and the bike are both part of the mass. The more weight a person has, the more force they need to move forward.
• Ball Falling through Air
  A ball falls through the air and lands on the ground. The force of the Earth’s pull on the ball is equal to the product of the ball’s mass and its speed due to gravity. This force is the same as the weight of the ball. More force will be put on a ball that is heavier.
•  Rock Rolling Down a Hill
  Gravity makes a rock roll down a hill. How fast it goes depends on how steep the hill is. A rock that is bigger and heavier will fall with more force.
• Pushing a Shopping Cart
  It is easier to push a shopping cart that is empty than one that is full. When the same force is used, a full shopping cart moves more slowly because it has more mass.
• Launching a Rocket
  To get into space, a rocket has to get past Earth’s gravity. The rocket is pushed with a lot of force. This thrust gives the rocket enough speed to get it high enough to leave Earth.
• Driving a Car
  Putting your foot on the gas pedal makes the car go faster (accelerator). The fuel flow to the engine is controlled by the gas pedal. So, letting more fuel gets burned in the engine gives the car the power and force it needs to speed up.
•  Racing Car
  A race car is made so that it has a low mass. So, the driver can pick up speed and speed up more quickly.
• Hitting a Ball
  In a baseball game, when a ball is hit with a bat, it goes as far as it can. The farther it goes depends on how hard it is hit. The ball moves in the same direction as the force.
• Pushing a Vehicle
  When the same force moves a car and a truck, the truck moves more slowly than the car because it is heavier.
  

Newtons Third Law of Motion

Newton’s third law of motion says that when a first object puts a force on a second object, the first object feels a force that is the same size as the force it puts on the second object but goes in the opposite direction. Newton’s third law of motion says that forces always come in pairs and that an object can’t push on another object without getting a force back of the same strength.

We sometimes call these pairs of forces “action-reaction pairs,” where the force that is put out is the action and the force that comes back is the reaction (although which is which depends on your point of view). You can use Newton’s third law to figure out which forces are outside of a system. Remember that when setting up a problem, it’s important to find the external forces because you have to add them up to find the net force.

Mathematical derivation of Newton’s 3rd Law of motion

Let A be the body putting out force. This is how Newton’s third law of motion is shown in mathematical form:

on body B, body B also puts out a force on body A, which is given as:

So, by comparing both forces we will get a final expression

Newton’s third law of motion is about how momentum stays the same. The law says that for every action, there must be a reaction that is equal and opposite to it.

Newton’s Third Law Examples and Applications

• As a teacher walks around in front of a whiteboard, he pushes against the floor in a backward direction. The floor gives the teacher a reaction force in the forward direction, which makes him move forward faster. In the same way, a car speeds up when the wheels push backward on the ground and the ground pushes forward on the wheels. When tires spin on a gravel road and throw rocks backward, this shows that the wheels are moving backward.
• The force that a baseball has when it hits a bat. Helicopters get a lift by pushing air down, which causes the air to push back up. Birds fly by pushing air in the opposite direction of where they want to go. For example, in order to get lift and move forward, a bird’s wings push air down and backward. The way an octopus moves through the water is similar to how a jet ski moves: it shoots water backward through a funnel in its body. In these cases, the octopus or jet ski pushes the water back, and the water pushes the octopus or jet ski forward.
• One example of an action-reaction pair is the way fish move through the water. A fish moves water backward with its fins. The fish moves faster because of this push. The force on the water is the same as the force on the fish, and the force on the water is going in the opposite direction of the force on the fish (forwards).
• The bird’s flight is an example of an action and its result. The air is pushed down by the bird’s wings. The air is pushed up by the air.
• A swimmer pushes against the water, and the water pushes back on the swimmer.
• Helicopters get a -lift by pushing the air down, which makes the air react by going up.
• Rock climbers push themselves up by pulling their vertical rope down.

FAQ’s

More Articles