Physical Quantity –
Quantities expressed in terms of laws of physics are called Physical Quantities. There are two types of Physical quantities. They are:
(i) Scalars – The physical quatities which has only magnitude and does not depend on direction is called Scalar quatities. For e.g. length, volume, speed, mass, density, temperature etc.
(ii) Vectors – Vector quantities has both magnitude and direction. For e.g. Displacement, velocity, Accelaration, Momentum etc
NOTE: A physical quantity which has both magnitude and direction but doesn’t obey vector law of addition or subtraction is not a vector quantity. For e.g. Electric current, pressure, work etc.
Unit of measurement – A quantity which is used as a standard of measurement is called Unit of measurement. There are usually two types of units –
(i) Fundamental unit – All those units which are independent of any other unit are called Fundamental units. There are seven fundamental units. They are:
| Fundamental Unit | SI Unit | Symbol |
|---|---|---|
| Length | Metre | m |
| Mass | Kilogram | kg |
| Time | Second | s |
| Temperature | Kelvin | k |
| Amount of substance | Mole | mol |
| Electric Current | Ampere | A |
| Luminuous Intensity | Candela | Cd |
| Plane Angles | Radian | Rad |
| Solid Angles | Steradian | Sr |
(ii) Derived Units – All those units which are expressed
in terms of two or more fundamental units is
called Derived Units. For e.g. velocity (m/s),
Accelaration, Force etc.
Dimensions of Physical Quantities – The dimensions of
a physical quatity are expressed in terms of powers of
Fundamental quantities. For e.g.Velocity=L/T=[LT1]=[M0LT-1].
KINEMATICS
Kinematics is branch of mechanics which deals with
the study of motion of the objects without taking into
account the cause of their motion.
Rest and Motion
An object is said to be at rest if it does not change its
position which respect to its surroundings with time
and said to be in motion if it changes its position with
respect to its surrounding with time.
- Rectilinear motion moving car on horizontal road, motion under gravity etc.
- Angular motion such as particle going on a circle, projectile motion, rotation of machine shaft etc.
- Rotational motion such as motion of a fan.
- It an object travels equal distances in equal intervals of time, then it is said to be in uniform motion.
- It an object travels unequal distances in equal intervals of time, then it is said to be in nonuniform motion.
Speed
• The distance covered by a moving body in a unit
time interval is called its speed.
• Speed = Distance travelled/ Time taken
• When a body travels equal distances with speed
𝑣1 and𝑣2
, then average speed is the harmonic
mean of the two speeds.
•
2 /𝑣
=
1/ 𝑣1
+
1 /𝑣2
⇒ 𝑣 =
2𝑣1𝑣2 /[𝑣1+𝑣2]
• When a body travels for equal times with speeds
𝑣1 and 𝑣2
, then average speed is the arithmetic
mean of the two speeds.
• 𝑣 = (𝑣1+𝑣2 )/2
Velocity
• The time rate of change of displacement of a
body is called its velocity.
• Velocity =
Displacement /Time
• An object is said to be moving with uniform
velocity if it undergoes equal displacements in
equal intervals of time.
• An object is said to be moving with non-uniform
or variable velocity if it undergoes unequal
displacement in equal intervals of time.
• Average velocity =
Time displacement/ Total time taken
Acceleration
• The time rate of change of velocity of a body is
called its acceleration.
• Acceleration = Change in velocity /Time taken
• It is a vector quantity and its SI unit is 𝑚𝑠
−2
.
• Acceleration at an instant of time is known as
instantaneous acceleration.
• When the velocity of a body increases with time,
then its acceleration is positive and if velocity
decreases with time, then its acceleration is
negative called deceleration or retardation.
• If acceleration does not change with time, it is
said to be constant acceleration.
Equations of Uniformly Accelerated Motion (Along
straight line)
If a body started its motion with initial velocity u and
attains final velocity v in the interval t. The
acceleration assumed to be uniform in motion is a
and the distance travelled is s, then equations of
motion:
• 𝑣 = 𝑢 + 𝑎𝑡
• 𝑠 = 𝑢𝑡 +
1/ 2 (𝑎𝑡
2)
• 𝑣
2 = 𝑢
2 + 2𝑎𝑠
• If any body is falling freely under gravity, then a is
replaced by g in above equations.
• If an object is thrown vertically upward, then in
above equations of motion a is replaced by (–g).
• For a body with zero acceleration or constant
speed, graph between velocity and time will be a
line parallel to time axis.
• Velocity–Time Graph For accelerating or
decelerating body the graph will be a straight line
inclined to time axis and velocity axis.
• Graph between position (distance)-time for an
accelerating or decelerating body is always a
parabola.
• Acceleration-time graph for uniformly
accelerating body is a line parallel to time axis.
• In case of uniform accelerated, the graph
between position and velocity is always
parabola.
• In case of uniformly accelerated motion, the
graph between velocity and time is always a
straight line.
• Slope of displacement-time graph gives velocity
and slope of velocity-time graph gives
acceleration.
Projectile Motion
• When a body is thrown from horizontal making an
angle (θ) except 90°, then its motion under gravity
is a curved parabolic path, called trajectory and
its motion is called projectile motion.
Examples:
• The motion of a bullet shot from the gun
• The motion of a rocket after burn-out
• The motion of a bomb dropped from a aeroplane
etc.
Properties of Projectile Motion
If we drop a ball from a height and at the same time
thrown another ball in a horizontal direction, then
both the balls would strike the earth simultaneously at
different places.
Circular Motion
• The motion of an object along a circular path is
called circular motion.
• Circular motion with a constant speed is called
uniform circular motion.
• The direction of motion at any point in circular
motion is given by the tangent to the circle at
that point.
• In uniform circular motion, the velocity and
acceleration both changes.
• In case of non-uniform circular motion, the speed
changes from point to point on the circular track.
• Angular Displacement – Angular displacement of
a body is the angle in radians through which
body revolves. It is represented by θ.its S.I. unit is
radian.
• Angular Velocity – If a body describes an angular
displacement in a particular time period, than
rate of velocity s known as Angular velocity. It is
represented by ω. ω = θ/t.
• Projectile Motion – If a body is projected upward
with a certain velocity, then the body describes a
path called trajectory path which is parabolic
and the motion is known as Projectile motion. A
projectile motion is influenced by downward
force of gravity.
Centripetal Acceleration
During circular motion an acceleration acts on the
body towards the centre, called centripetal
acceleration.
The direction of centripetal acceleration is always
towards the centre of the circular path.
Force
It is an external push or pull with can change or tries
to change the state of rest or of uniform motion. SI
unit is newton (N) and CGS unit is dyne. 1 N = 105
dyne.
If sum of all the forces acting on a body is zero, then
body is said to be in equilibrium.
Centripetal Force
During circular motion a force always acts on the
body towards the centre of the circular path, called
centripetal force.
F=mv2/r=mω2r.
Centrifugal Force
In circular motion we experience that a force is
acting on us in opposite to the direction of
centripetal force called centrifugal force. This is an
apparent force or imaginary force and also called a
pseudo force.
Applications of centripetal and centrifugal forces
• Cyclist inclined itself from vertical to obtain
required centripetal force. To take a safe turn
cyclist slower down his speed and moves on a
path of larger radius.
• Roads are banked at turns to provide required
centripetal force for taking a turn.
• For taking turn on a curved road, the frictional
force is acting between the tyres of the vehicle
and the road acts as centripetal force.
• If a bucket containing water is revolved fast in a
vertical plane, the water may not fall even when
bucket is completely inverted because a
centrifugal force equal or greater than the weight
of water pushes the water to the bottom of the
bucket.
• For orbital motion of electrons around the nucleus
electrostatic force of attraction is acting between
the electrons and the nucleus as centripetal
force.
• Cream is separated from milk when it is rotated in
a vessel about the same axis. During rotation
lighter particles of cream experience a lesser
force than the heavier particles of milk.
• For revolution of the earth around the sun,
gravitational force of attraction between the
earth and the sun acts as centripetal force.
Newton’s Laws of Motion:
Newton’s First Law
A body continues in its state of rest or of uniform
motion in a straight line unless an external force acts
on it. It is based on law of inertia.
Inertia is the property of a body by virtue of which is
opposes any change in its state of rest or of uniform
motion in a straight line.
Inertia of Rest
• When a bus or train at rest starts, to move
suddenly, the passangers sitting in it jerk in
backward direction due to their inertia of rest.
• The dust particles come out from a carpet when it
is beaten with a stick due to their inertia of rest.
• A passenger jumping out from a rapidly moving
bus or train is advised to jump in forward direction
and run forward for a short mile due to inertia of
rest.
Inertia of Motion
When a running bus or train stops suddenly, the
passengers sitting in it jerk in forward direction due to
inertia of motion
Momentum
The momentum of a moving body is equal to the
product of its mass and its velocity.
Conservation of Linear Momentum
The linear momentum of a system of particles remains
conserved if the external force acting on the system is
zero.
• Rocket propulsion and engine of jet aeroplane
works on principle of conservation of linear
momentum. In rocket, ejecting gas exerts a
forward force which helps in accelerating the
rocket upward.
Newton’s Second Law .
The rate of change of momentum of a body is
directly proportional to the force applied on it and
change in momentum takes place in the direction of
applied force.
𝐹 =
∆𝑝/ ∆𝑡
=
𝑚∆𝑣/ ∆𝑡
= 𝑚𝑎
Newton’s Third Law
For every action, there is an equal and opposite
reaction and both act on two interacting objects.
Rocket is propelled by the principle of Newton’s third
law of motion.
Impulse
• A large force which acts on a body for a very
short interval of time and produces a large
change in its momentum is called an impulsive
force.
• Its unit is newton-second.
• A fielder lowers its hand when catching a cricket
ball because by lowering his hands, he increases
the time of contact for stopping the ball and
therefore fielder has to apply lesser force to stop
the ball. The ball will also exert lesser force on the
hands of the fielder and the fielder will not get
hurt.
• Wagons of a train are provided with the buffers to
increase the time of impact during jerks and
therefore, decreases the damage. The vehicles
like scooter, car, bus, truck etc. are provided with
shockers.
Friction
Friction is a force which opposes the relative motion
of the two bodies when one body actually moves or
tries to move over the surface of another body.
The cause of friction is the strong atomic or molecular
forces of attraction acting on the two surfaces at the
point of actual contact.
Uses of Friction
• A ball bearing is a type of rolling-element that
uses balls to maintain the separation between the
bearing races. The purpose of a ball bearing is to reduce rotational friction and to support loads
(weight).
• Friction is necessary for walking, to apply brakes in
vehicles, for holding nuts and bolts in a machinery
etc.
• Friction can be decreases by polishing the
surfaces by using lubricants or by using ball
bearings.
• Tyres are made of synthetic rubber because its
coefficient or friction with road is larger and
therefore, large force of friction acts on it, which
stops sliding at turns.
• The tyres are threading which also increases the
friction between the tyres and the road.
• When pedal is applied to a bicycle, the force of
friction on rear wheel is in forward direction and
on front wheel is in the backward direction.
Loses due to Friction
• Too much Loss of Energy in machines and then
ultimately the machines are damaged.
Machine–
• Lever - It is a simple machine in which a straight or
inclined rod is made to turn or rotate at a point
freely or independently. There are three points
related to lever namely load, effort and fulcrum.
• Load - The weight carried by the lever is called
load.
• Effort - To operate lever, the force applied
externally is called effort.
• Fulcrum - The fixed point about which the rod of
lever moves independently is called fulcrum.
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