# Table of Units and Dimensions of Physical Quantities PDF

Table of Units and Dimensions of Physical Quantities PDF

# Physical Quantities

All quantities that can be measured are called physical quantities. eg. time, length, mass, force, work done, etc. In physical, we study about physical quantities and their inter relationship

# Measurement

Measurement is the comparison of a quantity with a standard of the same physical quantity.

# Units

All physical quantities are measured w.r.t. standard magnitude of the same physical quantity and these
standards are called UNITS. eg. second, meter, kilogram, etc.

So the four basic properties of units are:—
1. They must be well defined.
2. They should be easily available and reproducible.
3. They should be invariable e.g. step as a unit of length is not invariable.
4. They should be accepted to all.

# Set of Fundamental Quantities

A set of physical quantities which are completely independent of each other and all other physical quantities
can be expressed in terms of these physical quantities is called Set of Fundamental Quantities.

 Physical Quantity Units (SI) Units (CGS) Notations Mass kg g M Length m cm L Time s s T Temperature K (Kelvin) °C θ Current A A I or A Luminous Intensity cd (Candela) – cd Amount of Substance mol – mol

Dimensional of a physical quantity quantity are the powers, to which a Fundamental unit is raised, to obtain the unit of that physical quantity. The dimensional formula of a quantity as expressed in terms of Fundamental quantities, commonly mass M, length L and time T.

Any physical quantity is either a scalar or a vector.

# Scalar Quantities

Physical quantities which have magnitude only and no direction are called scalar quantities. Example – Mass, speed, volume, work, time, power, energy etc.

# Vector Quantities

Physical quantities which have magnitude and direction both and which obey triangle law are called vector quantities. Example – Displacement, velocity, acceleration, force, momentum, torque etc.

Note : (1) Electric current, though has a direction, is a scalar quantity because it does not obey triangle law.

(2) Moment of inertia, refractive index, stress are tensor quantities.

# Kinematics

It is the branch of mechanics, which deals with the motion of object.

# Distance

• The length of the actual path covered by a body in a particular time interval is called distance. It is always positive.
• It is a scalar quantity which has magnitude only. Its unit is metre.

# Displacement

• The difference between the final and the initial position of an object is called displacement. It may be positive, negative or zero.
• It is a vector quantity which has both magnitude and direction. Its unit is also metre.
• The magnitude of displacement may or may not be equal to the path length traversed by an object.

Displacement <= Distance

Speed

• Speed is the distance covered by a moving body in unit time.
• It is a scalar quantity. It is always equal to or greater than magnitude of the velocity.
• The average speed of a particle for a given interval of time is defined as the ratio of total distance travelled to the total time taken.

Average Speed = Total distance travelled / Total Time taken

• If the body covers first half distance with speed v1 and next half with speed v2, then

Average Speed = 2v1v2 / (v1 + v2)

# Velocity

• The rate of change of distance is called velocity.
• Velocity is a vector quantity, which has both magnitude and direction. Its unit is m/s.
• It may be positive or negative.

Average Velocity = Total displacement / Total time

• If the body covers first half distance with speed v1 and next half with speed v2, then
• Average Speed = 2v1v2 / (v1 + v2)

• If a body travels with uniform velocity v1 for time t1 and with uniform velocity v2 for time t2, then

Average velocity = (v1t1 + v2t2) / (t1+t2)

• If a body is moving on a circular path, then after completing one complete cycle, its average velocity is zero.

# Uniform Velocity

An object is said to be moving with uniform velocity if it undergoes equal displacements in equal displacements in equal interval of time.

# Non-uniform Velocity

An object is said to be moving with non-uniform or variable velocity if it undergoes unequal displacements in equal interval of times.

# Acceleration

• It is the rate of change of velocity. Its SI unit is m/s2. It is a vector quantity.
• 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.
• If velocity of a body is decreasing, then the acceleration is called retardation or deacceleration.
• Acceleration of an object is zero, if it is at rest or moving with uniform velocity.

## Equation of Motion

(i) v = u + at

(ii) S = ut + (1/2)at2

(iii) v2 = u2 + 2as

## Equation of Motion Under Gravity

(a) Downward direction

(i) v = u + gt

(ii) h = ut + (1/2)gt2

(iii) v2 = u2 + 2 gh

(b) In upward motion, we take negative g(i.e. g = -9.8 m/s2)

(c) Distance travelled by a body in nth second

Snth= u + (2n-1)(a/2)

where, S = distance travelled

h = height, t = time

u = initial velocity

v = final velocity

a = acceleration

g = gravitational acceleration

t = time-interval

• If the body is thrown upwards, then it will rise until its vertical velocity becomes zero. Then the Maximum height attained is h = v2/2g

# Relative Velocity

• When two bodies are moving in the straight line, the speed (or velocity) of one with respect to another is known as its relative speed (or velocity).
• If in vacuum we throw two objects of different masses from the same height, they reach the earth at the same time.
• If rain drops are falling vertically with velocity v and a person is walking horizontally with a velocity u, then he should hold an umbrella at an angle θ with vertical given by tanθ = u/v to prevent himself from being wet.

# 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 ω, sometimes Ω = θ/t

If T = time period = time taken by the object to complete one revolution, n = frequency = number of revolution in one second, then

nT = l and ω = 2πr/T = ωr = angular speed × radius

# Projectile Motion

• When a particle is so projected that it makes certain angle with horizontal, then the motion of the particle is said to be projectile.
• Path of projectile is a parabola.
• The initial velocity u of the projectile can be resolved into two components.
• (i) u cosθ (horizontal direction)
• (ii) u sinθ (vertical direction)
• To achieve maximum range the body should be projected at an angle of 45°. Therefore, a long jumper takes jump at an angle of 45°.
• To achieve maximum height the body should be projected at angle of 45°.
• The horizontal range is the same whether the body is projected at θ or 90 – θ.
• When a body is dropped freely from the top of the tower and another body is projected horizontally from the same point, both will reach the ground at the same time.
• If we throw two balls of different masses in horizontal direction, then they will again reach on earth at the same time because both the balls will have zero velocity in vertical direction.

For the projectile motion,

Maximum Height (H) = (u2sin2θ)/2g

Horizontal Range (R) = u2sin2θ/g

Total Time of Flight (T) = 2usinθ/g

# Circular Motion

When an object moves along a circular path, then its motion is called circular motion as motion of top etc. If an object moves along a circular path with uniform speed, its motion is called uniform circular motion. It is accelerated even if the speed of the body is constant. The motion of a satellite is accelerated motion.

# Units and Dimensions of Some Physical Quantities

Candidates can find the units and dimensions of some important physical quantities in below tabulated form.

 Quantity SI Unit Dimensional Formula Density kg/m3 M/L3 Force Newton (N) ML/T2 Work Joule (J) (=N-m) ML2/T2 Energy Joule (J) ML2/T2 Power Watt (W) (=J/s) ML2/T3 Momentum kg-m/s ML/T Gravitational constant N-m2/kg2 L3/MT2 Angular velocity radian/s T-1 Angular acceleration radian/s2 T-2 Angular momentum kg-m2/s ML2/T Moment of inertia kg-m2 ML2 Torque N-m ML2/T2 Angular frequency radian/s T-1 Frequency Hertz (Hz) T-1 Period s T Surface Tension N/m M/T2 Coefficient of viscosity N-s/m2 M/LT Wavelength m L Intensity of wave W/m2 M/T3 Temperature kelvin (K) K Specific heat capacity J/(kg-K) L2/T2K Stefan’s constant W/(m2-K4) M/T3K4 Heat J ML2/T2 Thermal conductivity W/(m-K) ML/T3K Current density A/m2 I/L2 Electrical conductivity 1/Ω-m(=mho/m) I2T3/ML3 Electric dipole moment C-m LIT Electric field V/m (=N/C) ML/IT3 Potential (voltage) volt (V) (=J/C) ML2/IT3 Electric flux V-m ML3/IT3 Capacitance farad (F) I2T4/ML2 Electromotive force volt (V) ML2/IT3 Resistance ohm (Ω) ML2/I2T3 Permittivity of space C2/N-m2 (=F/m) I2T4/ML3 Permeability of space N/A2 ML/I2T2 Magnetic field Tesla (T) (= Wb/m2) M/IT2 Magnetic flux Weber (Wb) ML2/IT2 Magnetic dipole moment N-m/T IL2 Inductance Henry (H) ML2/I2T2

# SI Prefixes

The magnitude of physical quantity vary over a wide range. The mass of an electron is 9.1 × 10–31 kg and that of our earth is about 6 × 1024 kg. Standard prefixes for certain power of 10.
Table shows these prefixes :

 Power of 10 Prefix Symbol 12 tera T 9 giga G 6 mega M 3 kilo k 2 hecto h 1 deka da -1 deci d -2 centi c -3 milli m -6 micro µ -9 nano n -12 pico p -15 femto f

# Physical Symbols and Their Meaning

 Symbol Name θ Theta α Alpha β Beta γ Gamma δ Delta Δ Delta µ Mu λ Lambda Ω, ω Omega π Pi Ф, ф Phi ε epsilon Ψ Psi ρ Roh ν Nu η Eta σ Sigma τ Tau κ Kappa χ chi ≅ Approximately equal to