What is the motion?
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Motion
Physical
and direction are called scal:hich have
, Mass, spæd, volume,
quantities.
Work.
Quantities Physical quantities Which have
and direction both and triangle law
quantities.
Displacement. velocity. acceleraum, force
current, though has a direction. is a scalar
it does not obey triangle law,
of inertia, refracåve inde•; sums
tiOeS
; Distance is the length of actual path covered
nosing cbject in a given time interval.
l:cenient Shortest distance by bcx\y in
direction is called displacement.
is a scalar quantity whereas displacement is a
r quantity both having the same unit (metre)
[>-placernent may positi ve, ne gative Of zero whereas
istance is always In general, magnitude of
t S distance
Speed . Distance travelled by the moving object in unit
Distance
is called SB•ed ie.
ume
a scalar quantity and its SI unit is metre/second
an object covers half of the distance with uniform
v, and the other half with uniform v
fren Lhe average speed of Object is
Velcu•ity : Velocity of a moving object is defined the
åspixement of the object in unit time interval i.e. velocity
Displacement
a vector quantity and its SI unit is metre/ second.
Acceleration : Acceleration of an is defined as
oi change of velcxity of the object i.e. acceleration
Ounge in Velocity
S a vector quantity and its Sl units is metre / second2
If velocity with time then acceleration is
and is called retardation.
Equation of motion in one dimension
I. Motion with uniform velocity.
s=vt
Motion with uniform acceleration
In case of motion with uniform acceleration
average velocity —
2
u = initial velocity
v final velxity
acceleration
t —time
s distance in straight line / displacement
Circular Motion : If an object describes a circular path
(circle) its moti
moves n•ith uniform speed, its motion is uniform circular
circular motion is an accelerated motion
direction of velocity changes continuously,
magnitude of velocity i.e speed of the body
remains
unchanged
Angular velocity : The angle subtended by the ling S
joining the object from
angular velo city.
It is generally denoted by and
ti T time period time taker:’ by the
object to complete one revolution,
frequency = no. of revolutions in
one æcond,
In one revolution. the object travels 2nr distance,
Linear speed _
angular speed x radius
Newton’s laws of motion : Newton, the father of physics
established the laws of motion in his book “principia” in
1687.
Newton’s first law of motion : Every body maintains
its initial state of rest cr motion with uniform speed on a
straight line unless an external force acts on it.
First law is also called law Of Galiltn-‘ or law of inertia.
Inertia : Inertia ig the of a body by virtue of
which the body opposes change in its initial state of rest
or motion with uniform speed on a straight line.
Inertia isof two types]. Inertia of rest2. Inertiaof motion
Some examples of Inertialfirgt Law :
2.
3.
When a car or train starts suddenly, the passengers bend
backward,
When a running horse stops suddenly, the rider bends
forward.
When a coat/ blanket is beaten by a stick, the dust
particles are removed.
First law gives the definition of force,
Force : Force is that external which when actg on
a changes or tries to change the initial state of rest
or motion with uniform velocity of the body.
push, Pull, tension in a string, tension in a coiled spring,
action, reaction, normal reaction, friction are forces;
Momentum : Momentum is the measure of amount/
quantity of motion contained in body Clearly it is the
property of a moving body and is defined as the product of
mass and velocity of the body, i.e.
momentum mass * velocity
It is a vector quantity. Its Sl unit is kgm l’ s.
Newton’s second law of motion : The rate of change in
momentum of a body is directly proportional to applie4
force on the body and takes place in the direction of force.
If F fore applied, a acceleration produced and
m= mass of body then
F= ma.
Newton’s second law gives the magnitude/ strength of
force.
Newton’s first law is contained in the second law
Newton’s IT-Iird Law of Mahon To every action, there
rs an equal and opposite reaction.
Examples of law—I. Recoil of a gun 2. Motion of
rocket 3, Swimming 4. While drawing water from the well,
if the string breaks up the man drawing water falls back 5, It
is difficult to fix a nail on a freely wooden frame.
Principle of conservation of linear momentum : If no
external force acts on a system of bodies. the total linear
momentum of the system of bodies remains constant.
As a consequence, the total momentum of
and after collision remains the same.
Rocket works on the principle of conservation of linear
momentum.
Impulse : V•Vhen a large force acts on a b«dy for very
small time, then force is called impulsive force, Impulse is
defined as the product of force and time.
Impulse force x time change in momentum.
It is a vector quantity and its direction is the direction
of force. Its SI unit is newton second (Ns).
Force in a spring is gi ven as F kx where k is the
force constant.
If a spring of force constant k is cut into equal parts,
force constant of each part is “k.
Friction
The force which opposes the relative motion between
two bodies in contact is called friction.
Friction is of two types
2.
Static friction : The force Of friction which is introduced
when there is no relative motion is called a static friction.
Static friction is a self adjusting force. Its value
becomes maximum when the applied force on its body
is such that the body is about to slide. Maximum value
of static friction is called limiting friction,
Kinetic friction : The friction which acts when a body
slides over the surface of other body is called kinetic or
dynamic friction.
Kinetic friction is less than the limiting friction
Kinetic friction is independent of relative speed
between the bodies provided the speed is small,
Friction depends upon nature of contact surface. Due
to roughness, the friction increases.
Friction is independent of macroscopic area of contact.
Friction is proportional to the normal reaction.
Rolling friction : This kind of friction acts when a body
rolls over the surface of other body.
Rol ling Friction is much smaller than the kinetic friction.
Centripetal Force : When a body travels along a circular
path, its velocity changes continuously. Naturally an externa I
force always acts on the body towards the centre of the path.
The external force required to maintain the circular
motion of the body is called centripetal force.
If a body of mass m is moving on a circular path of radius
R with uniform spæ–ed v, then the required centripetal force,
F=mv2/R
Examples Of centripetal force
Ii a stone attached to a string is whirled •
path. the required centripetal force is supplied
For the motion Oi planets around the Sun.
centripetal force is supplied by the
attraction of sun.
For the motion of electron around the _
atom. the required centripetal force is supplied
electrostatic attraction produced by the
nucleus.
A cyclist negotiating a curved path bends towards the
centre of the path so that the horizontal corn
ponent
normal reaction on the cyclist by the ground
supply the required centripetal force.
Due to this reason the outer edge of a curved
road
raised- This is called banking of roads.
Centrifugal Force : In applying the Newton’s
motion, we have to consider some forces which can
assigned to any object in the surrounding, These force,
called pseudo force or inertial force. Centrifugal force
a pseudo force. It is equal and opvxsite to centriFtal force
Cream separator, centrifugal drier workon theprindple
of centrifugal force.
Centrifugal forev should not confused as the reaction
to centr#ætal force forces ofactjm and reacbOn
act on different bodies.
Moment of force : The rotational effect of a force on u
about an axis of rotation is as moment of
Moment of a force abou t an axis of rotation is
as the product of magnitude of force and the
distance of direction of force from the axis of rotation.
i.e. Moment of force = Force x moment arm
It is a vector quantity. Its SI unit is newton metre (Nn)
Centre of Gravity : The centre of gravity of a bai’f
that point through which the entire weight acts.
centre of gravity of a body does not change with the change
in orientation of body in space.
The weight of a acts through centre of gravity in
the downward direction. Hence a body can brought to
equilibrium by applying a force equal to its weight in the
vertically upward direction through centre Of gravity
Equilibrium : If the resultant of all the forces actirgon
a body is zero then the body is said to in equilibrium.
If a body is in equilibrium, it will either at rest Otin
uniform motion. If it is at rest, the equilibrium is called
otherwiM2 dynamic.
Static equilibrium is of the following three tYFS :
I, Stable Equilibrium : If on slight displacement fTÜ1
equilibrium position, a E»dy has tendency to regain its
original position, it is said to be in stable equilibrium
2. Unstable equilibrium : If on slight displacement
from equilibrium position, a body moves in the directidl
Of displacement and does not regain its original posidcn
the equilibrium is said to unstable In
equilibrium, the centre of gravity of the l»dy is at the highest
position.
3. Neutral Equilibrium : If on slight displacement from
equilibrium position a body has no tendency to come back to
its original posi tion or to move in the direction of displacement,
it is said to be in neutral equilibrium. In neutral equilibrium,
the centre of gravity always remains at the same height.
Conditions forstable Equilibrium:Forstableequilibrium
Of a body, the following two conditions should be fulfilled.
1. The centre of gravity of the body should be at the
minimum height.
2. The vertical line passing through the centre of gravity
of the body should pass through the base of the body.