Laws of Motion Notes PDF in English for Class 11, NEET and JEE Exams

Laws of Motion Notes PDF: Find below the important notes for the chapter, Laws of Motion as per the NEET and JEE Physics syllabus. This is helpful for aspirants of NEET and JEE and other exams during last-minute revision. Important notes for Laws of Motion Notes PDF cover all the important topics and concepts useful for the exam.

Laws of Motion Notes PDF

Laws of Motion Notes PDF

Newton’s laws of motion give a scientific relationship between the forces that act on a body and the changes that occur due to this force. Sir Isaac Newton formulated the laws of motion in the year 1686 in his book ‘Principia Mathematica Philosophiae Naturalis’.

Force and Inertia

Inertia: The property of an object by virtue of which it cannot change its state of rest or of uniform motion along a straight line its own, is called inertia. Inertia is a measure of mass of a body. Greater the mass of a body greater will be its inertia or vice-versa. Inertia is of three types:
  • Inertia of Rest: When a bus or train starts to move suddenly, the passengers sitting in it falls backward due to inertia of rest.
  • Inertia of Motion: When a moving bus or train stops suddenly, the passengers sitting in it jerks in forward direction due to inertia of motion.
  • Inertia of Direction: We can protect yourself from rain by an umbrella because rain drops can not change its direction its own due to inertia of direction.

Force: Force is a push or pull which changes or tries to change the state of rest, the state of uniform motion, size or shape of a body. Its SI unit is newton (N) and its dimensional formula is [MLT-2]. Forces can be categorized into two types:

  • Contact Forces: Frictional force, tensional force, spring force, normal force, etc are the contact forces.
  • Action at a Distance: Forces Electrostatic force, gravitational force, magnetic force, etc are action at a distance forces.

What are the Three Laws of Motion?

The Three Laws of Motion are:

  1. Newton’s first law: Newton’s first law of motion states that, if a body is in the state of rest or is moving with a constant speed in a straight line, then the body will remain in the state of rest or keep moving in the straight line, unless and until it is acted upon by an external force. 

  2. Newton’s second law: Newton’s 2nd law of motion states that the rate of change of momentum of a body is directly proportional to the force applied on it, and the momentum occurs in the direction of the net applied force.

  3. Newton’s third law: According to Newton’s third law of motion, to every action, there is always an equal and opposite reaction.

Newton’s First Law of Motion

Newton’s first law of motion implies that things cannot start, stop, or change direction all by themselves, and it requires some force from the outside to cause such a change. This property of massive bodies to resist changes in their state of motion is called inertia. The first law of motion is also known as the law of inertia. The state of motion or rest cannot be changed without applying force. If a body is moving in a particular direction, it will keep moving in that direction, until an external force is applied to stop it.

There are two conditions on which the First law of motion is dependent:

  • Objects at rest: When an object is at rest velocity (v= 0) and acceleration (a = 0) are zero. Therefore, the object continues to be at rest.
  • Objects in motion: When an object is in motion, velocity is not equal to zero (v ≠ 0) while acceleration (a = 0) is equal to zero. Therefore, the object will continue to be in motion with constant velocity and in the same direction.

Newton’s Second Law of Motion

Newton’s second law states that the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the object’s mass. Newton’s second law describes precisely how much an object will accelerate for a given net force. The momentum of a body is equivalent to the product of its mass and velocity.

For a body of constant mass m, Newton’s law formula is given as,

F = ma,

Where ‘F’ is the applied force, and ‘a’ is the acceleration produced, and m is the mass of the object

If the net force acting on a body is positive, the body gets accelerated. Conversely, if the net force is 0, the body doesn’t accelerate.

Newton’s Third Law of Motion

According to Newton’s third law of motion, to every action, there is always an equal and opposite reaction. Also, the action and reaction occur in two different bodies. When two bodies interact with each other, they exchange force, which is equal in magnitude but act in opposite directions. This law has a huge application in static equilibrium where the forces are balanced, and also for objects which undergo uniform accelerated motion.

To understand Newton’s third law with the help of an example, let us consider a book resting on a table. The book applies a downward force equal to its weight on the table. According to the third law of motion, the table applies an equal and opposite force to the book. This force occurs because the book slightly deforms the table; as a result, the table pushes back on the book like a coiled spring. Newton’s third law of motion implies the conservation of momentum.

Law of Conservation of Linear Momentum

The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.

Conservation of linear momentum formula mathematically expresses the momentum of the system remains constant when the net external force is zero.
Initial momentum = Final momentum

P= Pf

Example: Rocket is an example of variable mass following law of conservation of momentum.
Thrust on the rocket at any instant F = – u (dM / dt)
where u = exhaust speed of the burnt and dM / dt = rate 0f gases combustion of fuel.
Velocity of rocket at any instant is given by u = vo + u loge (Mo / M )
where, vo = initial velocity of the rocket,
Mo = initial mass of the rocket and
M = present mass of the rocket.
If effect of gravity is taken into account then speed of rocket
u = vo + u loge (Mo / M) – gt

Equilibrium Of Concurrent Forces

Equilibrium of a body is a state in which all the forces acting on the body are balanced (cancelled out), and the net force acting on the body is zero. The state of equilibrium is a very important concept to learn in physics. If the net resultant force acting on a body is zero, it means that the net acceleration of the body is also zero (from the second law of motion).

Types of equilibrium of concurrent forces:

  • Static equilibrium: This is the type of equilibrium in which the resultant of all the forces acting on the body is zero, i.e. the net acceleration of the body is zero, and the velocity of the body is also zero. It means that the body is at rest. So if a body is at rest and the net acceleration of it is zero, it means the body is in static equilibrium.
  • Dynamic equilibrium: This is the type of equilibrium in which the resultant of all the forces acting on the body is zero, i.e. the net acceleration of the body is zero, but the velocity of the body is not zero. It means that the body is moving with a constant velocity. So if the net force acting on the body is zero, and it is still moving with some constant velocity, the body is said to be in dynamic equilibrium.

Forces Static and Kinetic Friction

Friction is a force resisting relative motion and it occurs at the interface between the bodies, but also within the bodies, like in case of fluids. The concept of friction coefficient was first formulated by Leonardo da Vinci. The magnitude of the coefficient of friction is determined by the properties of the surfaces, surroundings, surface features, presence of the lubricant, etc.

Laws of Friction

There are five laws of friction and they are:

  • The friction of the moving object is proportional and perpendicular to the normal force.
  • The friction experienced by the object is dependent on the nature of the surface it is in contact with.
  • Friction is independent of the area of contact as long as there is an area of contact.
  • Kinetic friction is independent of velocity.
  • The coefficient of static friction is greater than the coefficient of kinetic friction.

When we see any object, we can see the smooth surface but when the same object is viewed under a microscope, it can be seen that even the smooth appearing object has rough edges. Tiny hills and grooves can be seen through the microscope, and they are known as irregularities of the surface. So, when one object is moved over the other, these irregularities on the surface get entangled giving rise to friction. More the roughness, more will the irregularities and greater will be the force applied.

Static Friction

It is an opposing force which comes into play when one body tends to move over the surface ofthe other body but actual motion is not taking place. Static friction is a self adjusting force which increases as the applied force is increased.

Laws Of Static Friction

  • First law: The maximum force of static friction is not dependent on the area of contact.
  • Second law: The maximum force of static friction is comparative to the normal force i.e., if the normal force increases, the maximum external force that the object can endure without moving, also increases.

Kinetic Friction

Kinetic friction is defined as a force that acts between moving surfaces. A body moving on the surface experiences a force in the opposite direction of its movement. The magnitude of the force will depend on the coefficient of kinetic friction between the two materials.

Friction is easily defined as the force that holds back a sliding object. The kinetic friction is a part of everything and it interferes motion of two or more objects. The force acts in the opposite direction to the way an object wants to slide.

If a car has to stop, we apply brakes and that is exactly where the friction comes into play. While walking, when one wants to suddenly come to a halt, friction is to thank again. But when we have to stop in the middle of a puddle, things get harder since friction is less there and cannot aid one so much.

Formula of Kinetic Friction:

Kinetic friction, fk = μk N
where μ k = coefficient of kinetic friction and N = normal force.
Kinetic friction is of two types:
(a) Sliding friction
(b) Rolling friction
As, rolling friction < sliding friction, therefore it is easier to roll a body than to slide.
Kinetic friction (fk) = μk R
where μk = coefficient of kinetic friction and R = normal reaction

Laws of Kinetic Friction:

  • First law: The force of kinetic friction (Fk) is directly proportional to the normal reaction (N) between two surfaces in contact. Where, μk​ = constant called the coefficient of kinetic Friction.
  • Second law: Force of kinetic friction is independent of shape and apparent area of the surfaces in contact.
  • Third law: It depends upon nature and material of surface in contact.
  • Fourth law: It is independent of the velocity of object in contact provided the relative velocity between the object and the surface is not too large.

Rolling friction

This happens when a disc or ball rolls over a surface. The reason for this seems to be the distribution of energy involved in the twisting of objects. The coefficient used for the Rolling friction is determined as Crr and is known as Dimensionless rolling resistance coefficient.

Laws of Kinetic Friction:

  • With the increase in smoothness, the force of rolling friction decreases.
  • Rolling friction is expressed as a product of load and constant to the fractional power.
  • Rolling friction force is directly proportional to load and inversely proportional to the radius of curvature.

Dynamics of uniform circular motion

In this motion, the body is moving at a constant speed. Let’s say the radius of the circular trajectory on which the body is moving is “r”, and the speed of the body is v m/s. The figure shows the body going from point A to point B in time “t”. The length of the arc from point A to point B is denoted by “s”.

Angular velocity of the body is defined as the rate of change of angle. It’s similar to velocity in the case of straight-line motion.  It is denoted by the Greek symbol \omega.

\omega = \frac{d\theta}{dt} \\

Using the relation given above for the angle covered.

\omega = \frac{d}{dt}(\frac{s}{r}) \\ = \omega = (\frac{ds}{dt})\frac{1}{r}  

S is the length of arc which is the distance covered by the body, 

V = \frac{ds}{dt}, where v is the speed of the body. 

Substituting the value in the equation, 

\omega = (\frac{ds}{dt})\frac{1}{r} \\ \omega = \frac{v}{r}

Uniform Circular motion

Bodies have a tendency to move in a straight line. For the bodies making a circular motion at a constant speed, there must be some force that keeps them on a circular path. Such a force is called the centripetal force. The reaction of this force is called centrifugal force. This means that both these forces are equal and opposite in direction.

Centripetal force and its applications

Centripetal force is the force acting on an object in curvilinear motion directed toward the axis of rotation or centre of curvature. The unit of centripetal force is newton. The centripetal force is always directed perpendicular to the direction of the object’s displacement. Using Newton’s second law of motion, it is found that the centripetal force of an object moving in a circular path always acts towards the centre of the circle.

Centrifugal force is given by, 

F = \frac{mv^2}{r}

It is known that \omega = \frac{v}{r}

Substituting this relation into the equation,

F = \frac{mv^2}{r} \\ = F = \frac{m(r\omega)^2}{r} \\ = F = mr\omega^2

 

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