Motion
Scalar Quantities:
Physical quantities which have magnitude only and no direction are called
scalar quantities.
Example: Mass, Speed, work, volume, time, power, energy etc.
Vector Quantities:
Physical quantities which have magnitude and direction both and which obey the
law of triangle are called vector quantities.
Example: Displacement, velocity, acceleration, force, momentum,
torque etc.
Electric current though have direction, is a scalar quantity
because it does not obey the triangle law.
Moment of inertia, pressure, reflective index, and stress
are tensor quantities.
Distance:
Distance is length of actual path covered by a moving object in a given time
interval.
Displacement:
Shortest distance covered by a body in a definite direction is called
displacement.
►Distance is a scalar quantity whereas displacement is a
vector quantities both having
the same unit
(meter).
►Displacement may be positive, negative or zero but distance
is always positive.
►In general magnitude of displacement ≤ distance.
Speed:
Distance travelled by a moving object in unit interval of time is called speed.
i.e.
Speed = Distance/ Time
It is a scalar quantity and its SI unit is meter/ second
(m/s)
Acceleration of the object is defined as the rate of change
of velocity of the object i.e.
Acceleration = Change in velocity / Time
It is a vector
quantity and its unit is meter/second2 (m/s2)
If velocity decreases with time then acceleration becomes
negative and is called retardation.
Circular Motion:
If an object describes a circular path (circle) then its motion called
circular motion. If object moves with a uniform circular speed, then its motion
called uniform circular motion.
Uniform
circular motion is an accelerated motion because then direction of velocity changes
continuously.
Angular velocity: The angle subtended by the line joining
the object from the origin of circle in unit time interval is called angular
velocity.
It is
generally denoted by w and w = θ/t
If T=
time period = time taken by the object to complete on revolution, n= no. of revolution in one second
Then nT =1 & w=2π / T = 2πn.
► In one
revolution, the object travels 2πr distance.
So, Linear speed is =wr = angular speed * radius.
Newton’s Laws of motion: Newton,
the father of physics has established the laws of motion in his book “principia”
in 1667.
Newton’s first law of motion: Every
body maintains its initial position of rest or motion with uniform speed in on
a straight line unless an external force acts on it.
► First law also called the law of Galilieo or law of inertia.
► Inertia: Inertia is the property of a body by virtue of
which the body opposes change in
initial state of rest
or motion with uniform speed on a straight line.
Inertia is or two
types namely (i) Inertia of rest (ii) Inertia of motion
Some examples of inertia:
(i)
When a car or a train starts suddenly, the passengers
bends backward.
(ii)
When a running horse stops suddenly, the rider bends
forward.
(iii)
When a coat/ blanket beaten by a stick, the dust
particles are removed.
► First law gives the definition of force.
► Force: Force
is that external cause which when acts on a body changes or tries to
change the
initial state of the body.
Momentum:
Momentum 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 having SI unit kilogram /s.
Newton’s second law of motion: The
rate of change in momentum of a body is directly proportional to applied force
on the body and it takes place in the direction of the force.
If F= applied force, a=
acceleration produced and m= mass of the body
Then, nF =ma.
► Newton’s
second law gives the magnitude of force.
► Newton’s
first law is contained in the second law.
Newton’s third law of motion: To every
action, there is an opposite and equal reaction.
Examples
of third law:
(i)
Recoil of a gun
(ii)
Motion of a rocket
(iii)
Swimming
(iv)
While drawing water from the well, if the
string breaks up then man drawing water falls back.
Principal 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 bodies after and before collision remains
the same.
Impulse: When
a large force acts on a body for a very small time, then force is called
impulsive force. Impulse is defined as product of force and time.
Impulse =
force* time = change in momentum.
► It is a vector quantity and its direction is direction of
force. Its SI unit is Newton
second(Ns).
Centripetal Force:
When a body travels along a circular path (circle), its velocity changes
continuously, naturally an external force always acts on the body towards the
center 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 moving on a circular path of radius R with uniform speed v, then the
required centripetal force, F =mv2/R
Centrifugal Force:
In applying Newton’s
laws of motion, we have to consider some forces which can not be assigned to
any object in the surroundings. These forces are called pseudo force or inertial
force.
Centrifugal force is such a pseudo force. It is equal and
opposite to centripetal force.
► Cream separator, centrifugal driver works on the principal
of centrifugal force.
► Centrifugal force should not be confused as the reaction
to the centripetal force because forces of action and reaction act on different
bodies.
Moment of Force:
The rotational effect of a force on a body about an axis of rotation is
described in terms of moment of force.
Moment of
force about an axis of rotation is measured as the product of magnitude of
force and the perpendicular distance of direction of force from the axis of
rotation.
i.e. Moment of force =Force*moment arm.
► It is a vector quantity.
► Its unit is Newton
meter (Nm).
Center of Gravity:
The center of gravity of the body is that point through which entire weight
of body acts. The center of gravity of a body does not change with the change
in the orientation of the body in the space.
The weight of a
body acts through center of gravity in the downward direction. Hence a body can
be brought to equilibrium by applying a force equal to its weight in the
vertically upward direction through center of gravity.
Equilibrium:
If the resultant of all the forces acting on a body is zero then the body is
said to be in equilibrium.
If a body is in
equilibrium, then it will be either in the state of rest or in uniform motion.
If it is at rest, the equilibrium is called static otherwise dynamic.
Static
equilibrium is of following three types:
(i)
Stable Equilibrium: If on slight
displacement from equilibrium position, a body regains its original position,
it is said to be in stable equilibrium.
(ii)
Unstable equilibrium: If on slight
displacement from equilibrium position,
a body moves in the direction of displacement and does not returns to
its original position, the equilibrium is said to be unstable equilibrium. In
this equilibrium the center of gravity of the body is at the highest position.
(iii)
Neutral Equilibrium: If on slight
displacement from equilibrium position a body has no tendency to come back to
the original position or to move in the direction of displacement, it is said
to be in neutral equilibrium, the center of gravity always remains at the same
height.
Condition for
stable Equilibrium: For stable equilibrium of a body, the following two
conditions should be fulfilled.
(i)
The center of gravity of a body should be at the
minimum height.
(ii)
The vertical line passing through the center of gravity
of the body should pass through the base of the body.
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