Newton’s laws of motion

In physics, we start from the basic quantities that define a motion. These include vectors like displacement, velocity and acceleration. Velocity can be calculated by finding the time derivative of displacement and similarly acceleration can be calculated by finding the time derivative of velocity. Such studies come under kinematics because they only talk about the motion and doesn’t care about what causes them. But the moment we start asking what causes a motion to start, stop or change, the study regime goes to dynamics.

Dynamics is governed by forces, most importantly the inertial force. In simplest words, inertial forces are the forces that are caused due to mass.Now just think of a block that is placed on your table. You give it a little push and it travels a certain distance. Now just think about a few questions-

• How much distance (s) it travelled?
• How much time (t) it took to travel that distance?

You can answer above questions by simple measurements and they are easily visualized.Now if we probe little deeper and try to find out the velocity (v) and acceleration (a) of the block during that event, we have to simply find out (ds/dt) and (dv/dt) respectively. All these quantities are measured under kinematics. Now let us ask little more complex questions-

• Why did the body even move?
• Would the same push make a bigger block move?
• And once it moves why on earth it has to stop after some time!!

All these questions are related to dynamics and cn only be answered once we get a grip on three laws popularly known as ‘Newton’s laws of motion’. Newton commonly known as the guy who noticed a falling apple, has given many more laws governing today’s physics. Newton gave three laws of motion which form the basis of dynamics.

Newton’s first law of motion

The first law of motion is related to inertia. “A body can’t move if it is in rest and it can’t stop if it is moving until and unless an external force is not applied on it.” If we extend the law a little further, “If a body is moving with a certain velocity, it can’t accelerate or decelerate until unless we apply an external force to it.”

Newton’s second law of motion

how the velocity of an object changes when it is subjected to an external force. The law defines a force to be equal to change in momentum (mass times velocity) per change in time. For an object with a constant mass m, the second law states that the force F is the product of an object’s mass and its acceleration a:

F = m * a

For an external applied force, the change in velocity depends on the mass of the object. A force will cause a change in velocity; and likewise, a change in velocity will generate a force. The equation works both ways.

Newton also developed the calculus of mathematics, and the “changes” expressed in the second law are most accurately defined in differential forms. (Calculus can also be used to determine the velocity and location variations experienced by an object subjected to an external force.)

Let us define two more quantities now, impulse and linear momentum. Impulse is integral of force (F) over a short time and linear momentum is the product of mass (m) and velocity (v). Second law of motion states that, “Change in momentum is equal to the impulse on a body.”

In the above equation, dv/dt denotes the linear acceleration (a). So, the equation becomes F=ma. Or the force applied on a body is equal to the mass of the body and acceleration of the body.

Newton’s third law of motion

Newton’s third law is a rather simple statement but really useful when finding the reaction forces on bodies. The law states that, “If a body applies force F on another body, the other body applies the same amount of force, opposite in direction on the first body.”

Above three laws govern all the dynamic part of mechanics. All the governing equations, as simple as moving block or as complex as a moving aeroplane, are governed by essentially these three laws.

Simplifying, it states that every action (force) in nature there is an equal and opposite reaction.