LAWS OF MOTION
A push or a pull exerted on any object, is defined to be a force. It is a vector quantity. Force can
be grouped into two types:
Contact forces are the forces that act between two bodies in contact, e.g. tension, normal
reaction, friction etc.
Non-contact forces are the forces that act between two bodies separated by a distance without
any actual contact. e.g. gravational force between two bodies and electrostatic form between
two charges etc.
External agencies (e.g. gravitational and magnetic forces) can exert force on a body even from a
distance.
Aristotelian law of motion: An external force is required to keep a body in motion.
Opposing forces such as friction (solids) and viscous forces (for fluids) are always present in
the natural world.
THE LAW OF INERTIA
Galileo studied motion of objects on an inclined plane.
Objects (i) moving down an inclined plane accelerate, while those (ii) moving up retard. (iii)
Motion on a horizontal plane is an intermediate situation.
Galileo concluded that an object moving on a frictionless horizontal plane must neither have
acceleration nor retardation, i.e. it should move with constant velocity. Also he concludes the
state of rest and the state of uniform linear motion (motion with constant velocity) are
equivalent. Ex:
Using Galileo law of inertia Issac Newton state fisrt law of motion (law of Inertia – defines
force) as
Every body continues to be in its state of rest or of uniform motion in a straight line unless
compelled by some external force to act otherwise. ( called as Inertia or ‘resistance to change’).
As inertia of a body is measured by the mass of the body. Heavier the body, greater the force
required to change its state and hence greater is its inertia. There are three type of inertia (i)
inertia of rest (ii) inertia of motion (iii) inertia of direction.
If the net external force on a body is zero, its acceleration is zero. Acceleration can be non zero
only if there is a net external force on the body.
NEWTON’S SECOND LAW OF MOTION
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. Second law relates the external force on a
body to its acceleration.
Thus, if under the action of a force F for time interval t, the velocity of a body of mass m
changes from v to v + v i.e. its initial momentum p = m v changes by p mv .
According to the Second Law,
where k is a constant of proportionality. Taking the limit t 0, the term p / t
becomes the derivative or differential co-efficient of p with respect to t, denoted by
dp/dt.
In SI unit force is one that causes an acceleration of 1 ms-2 to a mass of 1 kg. This unit is
known as newton:
1 N = 1 kg ms-2.
Momentum
Momentum of a body is defined to be the product of its mass m and velocity v, and is denoted
by p:
p = m v Momentum is clearly a vector quantity.
Impulse
Alarge force acts for a very short duration producing a finite change in momentum of the body
is called an impulsive force.
Impulse = Force × time duration
= Change in momentum
NEWTON’S THIRD LAW OF MOTION
To every action, there is always an equal and opposite reaction.
Force never occurs singly in nature. Force is the mutual interaction between two bodies. Forces
always occur in pairs Action and reaction forces act on different
bodies, not on the same body.
Two bodies as a whole, FAB and FBA are internal forces of the system (A + B). They add up to
give a null force. Internal forces in a body or a system of particles thus cancel away in pairs.
CONSERVATION OF MOMENTUM
The total momentum of an isolated system of interacting particles is conserved.
It states that if no external force is acting on a system, the momentum of the system remains
constant.
According to second law of motion, F =dp /dt
If no force is acting, then F = 0
dp/dt = 0 then p = constant
or m1v1 = m2v2 = constant
Equilibrium of a particle in mechanics refers to the situation when the net external force on the
particle is zero. According to the first law, this means that, the particle is either at rest or in
uniform motion.
