Newton's Law of Motion

Newton’s Laws of Motion

We know that force is a push or a pull which tends to change the state of motion of an object i.e. if an object is initially at rest then an applied force tends to bring it in motion and if an object is already in motion then a force acting on it can bring the object at rest or change its speed or change the direction of motion.

The relationship between force and motion can be best understood with the Newton’s Laws of motion.

It will be better if we try to understand the Galileo’s law of inertia first.

Law of Inertia: The tendency of an object to resist any change in its state of rest or uniform motion along a straight line is called inertia. In other words, if an object is at rest it continues to stay at rest and if an object is in motion it continues to remain in motion.

The measure of inertia is mass of an object. Higher the mass of an object, higher is its inertia i.e. higher is its tendency to resist any change in its state.

Inertia is of 3 types:

(1)    Inertia of rest

(2)    Inertia of motion

(3)    Inertia of direction

Newton’s First Law of Motion:

Newton’s first law is simply the law of inertia or we can say extension of law of inertia.

An object continues to be in a state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force.

The difference between Galileo’s law of inertia and Newton’s first law of motion is that Galileo was not able to identify the cause or agent that can bring the change in state of motion or rest. Whereas Newton’s identify that unless an external force acts on an object its state cannot be changed.

Examples of Newton’s first law:

(a)    When a bus starts suddenly from rest passengers tends to fall backwards.

(b)   When a moving bus stops suddenly passengers tends to fall forward.

(c)    An athlete continues to run further even after crossing the finishing line.

(d)   When a carpet is beaten with a stick dust particles comes out.

(e)   If we hit a striker on a pile of carom coins only the bottom most coin will move with the striker.

Before we start second law of Newton let us discuss an important physical quantity known as momentum.

Momentum: The product of mass and velocity of an object is known as momentum. It is denoted by letter p and it is a vector quantity.

P = mv

The momentum simply gives us the idea of quantity of motion an object possesses. A bullet of small mass moving with very high velocity possesses huge momentum because of its velocity. Whereas a truck moving with slow speed possesses large momentum due to its huge mass.

Newton’s 2^nd Law

The first law of Newton’s identifies the force that it is the cause of motion or change in state of motion. The Newton’s 2^nd law gives the mathematical expression for that force.

The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of force.

Consider an object of mass m moving with velocity u. A constant force F acts on an object for a small time t such that its velocity increases from u to v.

\[Change\ in\ momentum = mv - mu \]
\[Rate\ of\ change\ of\ momentum = \frac{mv - mu}{t}\]
According to second law, the rate of change of momentum is directly proportional to the applied unbalanced force.

\[\frac{mv-mu}{t}∝F\]
\[F∝\frac{mv-mu}{t}\]
\[F∝m\frac{v-u}{t}\]
\[F∝ma\]
\[F=kma\]

Where k is a constant. The unit of Force is so chosen such that the value of k becomes 1. Thus
\[F=ma\]

The SI unit of force is newton (N). 1N is that force which when applied to a mass of 1 kg produces an acceleration of 1 m/\(s^2\) in it.

Examples of Newton’s 2^nd law

(a)    In cricket, while catching a fast moving ball, the fielder gradually lowers his hands with the ball. This is done to increase the time in which the final velocity of the ball becomes zero. This reduces the rate of change of momentum thereby decreasing the force exerted by ball on the hands of the player.

(b)   A karate player moves his hands very fast while breaking a pile of tiles.

(c)    Delicates items are wrapped in thermocol.

(d)   In a high jump, the athletes are made to fall on a cushion bed.

Newton’s Third Law of motion

For every action, there is equal and opposite reaction.

It means when one object exerts a force on another object then the second object instantaneously exerts equal and opposite force on the first. These two forces are equal in magnitude but opposite in direction.

The action and reaction forces act on different object (not on the same object).

Examples of Newton’s Third law

(1)    When a gun is fired the bullet moves in the forward direction and the gun recoils in the opposite direction. Here gun applies force on the bullet in the forward direction and the bullet apply equal and opposite force on the gun in the backward direction.

(2)    When we walk on the road we apply force on the road in the backward direction and the road pushes us in the forward direction.

(3)    When we jump we apply force on the ground in downward direction and the ground apply equal and opposite force on us in the upward direction.

(4)    During the flight of a bird, the bird pushes the air downward with its wings and the air applies equal and opposite force on the wings in the upward direction.

(5)    While swimming, we apply force on the water in the backward direction. It is reaction force of water that pushes us in the forward direction.