Newton’s first law of motion (law of inertia):

Every inanimate body continues to be in its state of rest of state or state of uniform motion in a straight line unless compelled by some external force.

Newton’s second law of motion (law of momentum):

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

Newton’s third law of motion (law of action and reaction):

To every action there is a reaction. Action and reaction are equal opposite and simultaneous.

Momentum (p):

Momentum is defined as product of mass and velocity. It is a vector quantity.

p = m . v

where p = momentum, m = mass, and v = velocity. Its SIU is kg.m/s. Bold letter represents vector quantity.

Force (f):

Force is defined as rate of change of momentum. It is also defined as product of mass and acceleration. It is a vector quantity.

f = m . a

where f = force, m = mass, and a = acceleration. Its SIU is N or newton. 1 N = 1 kg.m/s². Bold letter represents vector quantity.

Impulse (J):

Impulse is defined as change in linear momentum of the object. It is also defined as product of force and time. It should be noted that impulse is a large force applied for a very short interval of time. It is a vector quantity and its direction is same as that of force. Its SIU is N.s.

J = dp/dt = f . t

where dp/dt = rate of change of momentum, f = force, t = time. Bold letter represents vector quantity.

Real force:

A force which is produced due to interaction between the objects is called real force. Examples: gravitational force, electromagnetic force, strong nuclear force, frictional force, etc.

Pseudo force:

An imaginary force assumed in accelerated frames of reference so that Newton’s laws can be explained satisfactorily in accelerated frames of reference.

Notice that modern text-books of Physics avoid using the terms “real force” and “pseudo force.” For example, the book "Principles of Physics" by Halliday and Resnick has not mentioned the terms "pseudo force" and "centrifugal force" (centrifugal force is the most common example of a pseduo force) anywhere in their book. However, in everyday life, the term "centrifugal force" continues to be very popular.

Fundamental forces in Physics:

There are four fundamental forces in Physics as follows: (a) gravitational force, (b) electromagnetic force, (c) strong nuclear force, and (d) weak nuclear force.

Gravitational force:

The force which is responsible for the existence of solar system is called gravitational force. This force is always attractive in nature. The planets in solar system are bound to Sun because of gravitational attraction between Sun and planets. The range of this force is infinite. This force is weakest among all four fundamental forces. The magnitude of this force is given by Newton’s law of gravitation.

Newton’s law of gravitation:

Every particle (say, particle 1) attracts any other particle (say, par- ticle 2) with the force given by:

F = G . m1 . m2 / r²

where F = gravitational force between the particles, G = gravitational constant also called universal gravitational constant = 6.67 × 10^-11 N.m²2, m1 and m2 = masses of the particles 1 and 2, r = distance between the particles 1 and 2. The force acts along the line joining the two particles.

Electromagnetic force:

The force which is responsible for the existence of atoms is called electro- magnetic force. Electrons in an atom are bound to nucleus because of attractive electromagnetic force. There are positive and negative electric charges. This force is repulsive between like charges (i.e., positive-positive or negative-negative) and attractive between unlike charges (i.e., positive- negative or negative-positive). The range of this force is infinite. This force is second strongest among all four fundamental forces. The magnitude of this force is governed by Coulomb’s law.

Coulomb’s law of electrostatics:

The magnitude of force between two charged particles 1 and 2 is given by:

F = k . q1 . q2 / r²

where F = electrostatic force between the particles 1 and 2, k = Coulomb's constant = 8.99 x 10⁹ N.m²/C², q1 and q2 = electric changes on particles 1 and 2, r = distance between the particles 1 and 2. The force acts along the line joining the two particles. Also notice that Coulomb's constant k is related to permittivity of free space ε₀ (ε₀ = 8.85 x 10^-12 F/m) by the following relation:

k = 1 / (4 π ε₀)

Strong nuclear force:

The force which is responsible for the existence of nucleus is called strong nuclear force. This force is attractive in nature. The nucleons (nucleons means ingredients of nucleus, i.e., protons and neutrons) are bound together because of strong nuclear force. Despite repulsive Coulombian forces between positively charged protons, this force tightly binds the nuceons together. This is, however, a short range force and effective within nuclear-scale distances. This force is strongest among all four fundamental forces.

Weak nuclear force:

The force which is responsible for the beta decay (beta decay means spontaneous emission of electrons) from some radioactive materials is called weak nuclear force. This is also a short range force and effective within nuclear scale distances. This force is third strongest among all four fundamental forces.

Inertial frame of reference:

A frame of reference in which Newton’s first law of motion (i.e., law of inertia) holds good is called inertial frame of reference.

Non inertial frame of reference:

A frame of reference in which Newton’s first law of motion (i.e., law of inertia) does not hold good is called non-inertial frame of reference. An accelerated frame is an example of non-inertial frame of reference.

Law of conservation of linear momentum:

Law of conservation of linear momentum states that in an isolated system the total linear momentum of the system of interacting bodies remains constant or conserved.

Example of conservation of linear momentum:

Let the bodies 1 and 2 of masses m1 and m2 suffer an elestic collision, and let u1 and u2 be their velocities before collision and let v1 and v2 be their velocities after collision then according to this law, we have (bold letter represents vector quantity):

(m1 . u1) + (m2 . u2) = (m1 . v1) + (m2 . v2)

Relation between work and force:

The relation between work and force is given by the following expression:

W = f . s

where, W = work, f = force, and s = displacement. Work is scalar quantity. Force and displacement are vector quantities. The dot product (scalar product) of force and displacement is performed to get the work.

Elastic collision:

The collision in which total kinetic energy of the colliding bodies is conserved (i.e., is the same before and after the collision) is said to be elastic collision.

Inelastic collision:

The collision in which total kinetic energy of the colliding bodies is not con- served (i.e., is not the same before and after the collision) is said to be inelastic collision.

Coefficient of restitution (e):

Coefficient of restitution (e) is defined as the ratio of relative velocity of separation after collision to the relative velocity of approach before collision between two colliding bodies.

Rigid body:

A body is said to be rigid if the relative distance between any two particles of the body does not change under application of force of any magnitude.

Torque (or moment of force):

The ability of a force to produce a rotational motion is called a torque (or moment of force). Torque is given by the following expression:

τ = r × f

where τ = torque, r = position vector that connects axis of rotation to point where force is applied, and f = force. Torque, moment arm, and force are vector quantities. The vector product of r and f gives us τ. Bold letter represents a vector quantity.

Couple:

Two equal and parallel forces acting in opposite directions at two different points of a given body form a couple.

Centre of mass:

Centre of mass of a body is defined as that point at which the whole mass of the body is supposed to be concentrated, in order to study motion of the body in accordance with Newton’s laws of motion.

Centre of gravity:

Centre of gravity is a fixed point through which the whole weight of the body always acts vertically downwards, whatever may be the position of the body.

Equilibrium:

A rigid body is said to be in equilibrium if under the application of forces, it remains in state of rest or state of uniform motion.

Translational equilibrium:

A rigid body is said to be in translational equilibrium if the resultant force acting on the body is zero.

Rotational equilibrium:

A body is said to be in rotational equilibrium if the resultant torque acting on a body is zero.

Kinetic energy:

Kinetic energy (K.E.) of an object given by the following expression:

KE = (1/2) m v²

where KE = kinetic energy of an object, m = mass of an object, and v = velocity of an object. SIU of energy is joule or J and CGS unit of energy is erg. Energy is scalar quantity.

Gravitational potential energy:

Gravitational potential energy of an object is given by the following expression:

GPE = m . g . h

where m = mass of an object, g = gravitational acceleration due to earth = 9.81 m/s², h = height from the ground to the point where the object is placed (located). SIUnit of energy is joule or J and CGS unit of energy is erg. Energy is scalar quantity.

Relation between work and energy:

The relation between work and energy is as follows:

work = energy

Relation between work and power:

Rate of doing work is called power. Its expression is:

P = W / t

where P = power, W = work, and t = time. SIUnit of power is W or watt. 1 W = 1 J/s. In electrical engineering, SIUnit watt is quite popular, whereas in mechanical engineering, FPS unit horse power (its symbol is hp) is more popular. 1 hp = 746 watt (more accurately, 1 hp = 745.7 W).