Month of Equations: “What is the meaning of Newton’s second law of motion?”

9. Newton's Law

Meaning of the equation:

Newton’s second law states that the rate of change of momentum is directly proportional to the external force applied on that object.

Second out of the three famous Newton’s laws of motion, this law depicts a relationship between change in momentum and the external force applied on an object. Momentum which is defined as the product of mass and velocity of an object is also represented as the quantity of motion contained in a body. On the other hand, rate of change of momentum refers to the change in momentum per unit change in time. Newton’s second law states that the an external force applied on an object is proportional or in some cases equivalent to the change in momentum per unit time of the object.

Let’s consider  few simple example to understand it in detail:

  1. Assume that you are driving a car at a particular velocity. The momentum of the car-passenger system will be given by the product of mass and velocity of the car and given by some finite value p. Suddenly, a dog comes into your way and you need to immediately stop the car , i.e., you need to change the momentum of the car from p to zero in a blink of the eye. What will you do? Well, you will just apply breaks, but with much greater force as compared to the normal routine when you need to stop your car after reaching your destination. Hence, the more forcefully you apply the breaks, the lesser time would be required to change the momentum of an object by an equivalent value as it would normally change when you bring your car to a halt after reaching your office or the desired destinations.newton_fielder.jpg
  2. For those of you who love sports, let us consider another way of understanding it. Assume that you are playing cricket. While you are fielding, you run to catch a ball in order to out a batsman.  But before you stop the ball, you give the ball ample time to reach your hands by detracting your hands downwards and then catch it. What happened here?                                                                                                                                                       When you detracted your hands downwards, it gave the ball sufficient time for bringing its momentum down to zero from a particular value. The increase in time made the rate of change of momentum much smaller and hence less external force applied by the hands of the fielder and the fielder is prevented from any injury.

You see, we subconsciously encounter Newton’s second law many times in our day to day life without even realizing that we are making use of a famous law in Physics. It is rightly said that Physics is the study of nature and natural phenomenon.

Not only this, Newton’s second law also means that a change in motion certainly involves acceleration. This is true for objects moving with velocity much less than the speed of light such that the mass of the object remains constant in the given time interval and a change in momentum only refers to a change in velocity of the object or system. This directly seconds the Newton’s first law or the law of inertia which states that “An isolated system at rest or in uniform motion will continue to be in its state of rest or motion until an external force is applied on it”. Hence, a change in momentum will occur only if an external force is applied on the system and vice-versa.

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