 Newton’s Laws of Motion, Momentum Force General Knowledge

Newton’s Laws of Motion, Momentum Force related GK for you competitive examinations such as UPSC, IAS, Civil Service, Staff Selection Commission or SSC, CGL, MTS, Banking SBI PO, Railway etc. Dear aspirants, read this topic carefully. This is an important part of physics from which some questions may be listed on your question paper.

Contents

To describe the characteristics of motion we need to set up some laws, which enable us to understand or explain the motion of a particle. There are three fundamental laws provided by English physicist Sir Isaac Newton. He is the father of physics. He first established his three laws of motion in his book ‘Principia‘. According to his name three laws are named as Newton’s First law, Newton’s Second law and Newton’s Third law.

In this chapter we will first state the laws of motions then we well elaborate briefly. We will also see how force is defined from first law as well as how forced is measured from his second law.

Newton’s Laws of Motion:

Newtons First Law:

Every object continues in its state of rest or of uniform motion in a straight line if no net force acts upon it. This is also known as law of inertia.

Explanation: Let us consider a particle moves in a straight line. According to first law, the speed and direction will remain same unless the object faces to an external force. Here external force means the force applied on the object from outside. But wait, when we through a ball with an initial speed, its speed continue to decrease until it comes to rest. Here we do not apply any external force, then why it stops after travelling some distance? Well, though we do not exert any force from outside, a frictional force by air or ground comes to act on the ball. This friction is the cause to stop the ball from moving with constant speed in a straight line. This friction opposes the constant motion of the particle.

Definition of force from First Law: From first law we see that we need to apply an external force to change its motion. Thus force may be defined as follows. What we apply from outside to change the motion or to change shape, size or direction of an object is called force. Therefore force can change the velocity, shape or size of an object. SI unit of force is Newton. In c.g.s system unit of force is dyne. When frictional force applies on moving ball, it decreases the speed of the ball.

1 Newton force = 105 dyne.

Inertia from First Law:

Inertia is a property of a body by virtue of which the body opposes change in its initial state of rest or motion along straight line. First law state that motion of a body never change unless the application of force. Thus if a body is in rest it try to stay rest and if body is in motion it try to be in motion forever.

There are two types of inertia –

1. Inertia of rest
2. Inertia of motion

Inertia of rest: Inertia of rest means the body tries to stay in its rest state forever. Example: When a car or train starts moving suddenly the passengers bend backward. This is because when the train or bus moves suddenly our lower part of body start to move i,e, become dynamic but our upper part of body remain to its original static or rest state.

Inertia of motion: Inertia of motion means the body tries to stay in motion forever. Example: When a car or train stops suddenly we bend forward. Similarly in this case our lower part of body become rest as the train or bus stop but our upper part try to maintain its original motion.

To state the second law of motion we first need to introduce another physical quantity, momentum.

Momentum: In physics momentum is defined as the product of mass and velocity. It is a vector quantity as velocity is. SI unit of momentum is Kilogram-meter/second, or Kg-m/s.

Thus Momentum p = m*v,

m = Mass of object and v = velocity.

Now understand what actually momentum is. Let an empty truck (less mass) moving with greater velocity than a loaded truck (with greater mass) moving with less velocity. If both truck collide a wall, which truck will dismantle the wall more? If we take into account mass and velocity individually, it is hard to answer the question. Because it does not mean that more mass with less velocity will produce more damage than less mass with more velocity and vice versa. Thus another physical quantity is needed to introduce to explain this phenomenon. Momentum is a new kind of physical property of matter that arise when an object have some velocity and mass. Therefore multiplying mass by velocity, we can measure momentum.

Newton’s Second Law

The rate of change of momentum is directly proportional to the applied force on the body and takes place in the direction of force.

I have already told you that second law gives us the magnitude of force. Now let us see how to deduce the formula of force.

newton's second law of motion mathematical formula

Consider a particle of mass 'm' having initial velocity 'v1. After some time 't' velocity become v2. Then initial momentum is mv1 and final momentum is mv2.

Change of momentum Δp =  mv2 −  mv1

Rate of change of momentum, Δp/t = (mv2 −  mv1)/t

According to second law, Force ∞ Δp/

or, F ∞ (mv2 −  mv1)/t

or, F = k*(mv2 −  mv1)/, [Where 'k' = proportional constant;]

or F = k*m*(v2 −  v1)/t

or F = k*m* a; [Where a =  acceleration = (v2 −  v1)/t]

According to definition of 1 N force (to produce unit acceleration on unit mass, force required is one Newton) if mass is 1 kg, acceleration is 1 m/s2, and force is 1 N then the constant 'k' is 1.

Thus F = ma

This is the equation of force deduced from the second law of motion.

Newton’s Third law:

Newton’s third law is stated as “every action there is an equal and opposite reaction”.

The statement means that body A exerts a force on body B, then an equal and opposite force will also exert on body A by body B. Example: Suppose a gun fire a bullet. The gun exerts a force on bullet. According to third law the bullet also exert opposite and equal force on gun. That’s why when bullet is fired, the gun experience recoil in the backward direction. Other good examples of Newton’s third law are rocket propulsion and jet engine. Rocket contains solid fuel. Fuel burns and hot gasses propels out with very high velocity. This is an action. So the reaction of this force propels the rocket forward.

Impulse: Impulse is defined as the product of Force and time. Impulse is a vector quantity and its direction is along the direction of force.

Force F * Time t = Impulse = Change in momentum.

If the time of contact of two moving body is small then a large change of momentum occur producing a large impact of force.

Centripetal force: It is an external force that required maintaining the circular motion of a body. When a body moves circularly, its direction as well as velocity always changes. Therefore to changing velocity produce change of momentum. According to second law changing momentum gives us force. When an object rotates it always constitutes centripetal force that acts along the center of curvature. Centrifugal force: It is a Pseudo force and equal and opposite to centripetal force.

Moment of Force: Moment of force is an effect of rotation. Turning effect of an object about a point or an axis or rotation is known as moment of force. In our daily life we utilise the rotational effect. As an example, when we try to open a door by pushing nearer to hinges, larger force is required. Thus rotational effects depends of two factors –

1. How much force is applies i.e. magnitude of force;
2. And distance of force from the axis. More the distance from rotational axis less force is required. Thus moment of force is mathematically described as the product of the magnitude of force and the distance between the point on which force is applied and rotational axis.

Read: Gravitation – Physics > GK

Thus Moment of force = force × perpendicular distance;

It is a vector quantity. SI unit is Newton-meter (N-m).