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Work, Power and Energy

Work Power Energy > Important Physics GK [PDF]

Work, Power and Energy General Knowledge

Work, Power, and Energy-related important General knowledge and basic concept with the definition for UPSE, IAS, SSC CGL, MTS, Railway, Banking, and other competitive exams.

In general sense, work means any kind of physical and mental activity. Someone study very hard in his study room to get good marks in the examination. This is a mental activity. We always say that he is hard-working on the study. But in mechanics, work is not like that. In physics, it is defined by others away.

What is work in Physics?

In physics or mechanics, when a body gets displaced by application of force on it, we say that work is done.

How much work is done?

Work done is measured as the product of displacement of a body and the force applied to it due to which it displaced. Due to the application of force F, an object displaced at a distance s, work done is –

W = Fs ; Which is the formula of work done.

Force and displacement are vector quantities. Dot vector product of force F and displacement s gives us the amount of work done. The dot product of two vectors is always scalar. Thus work is a scalar quantity.

If the direction of force and displacement is different, i,e. the direction of force and displacement make an angle θ between them, then according to vector dot product rule, work done is governed by –

W = |F| × |s| cosθ ; |F| is the magnitude of force and |s| is magnitude of displacement.

Work done – examples

If displacement is zero, the work done is zero. A man pushing a wall and get tired, he is not doing any work since the wall is in a stable position.

example of work done on an object

Again we see that if the angle between force and displacement is 90° then cosθ = cos90° = 0. The work done is zero. Earth is moving around the sun. The direction of gravitational force and displacement of the earth is 90°. Hence no work is done on or by the earth.

Both force and displacement are the same directions, the work done is maximum i.e. W = FS. SI and C.G.S system the unit of work done is Joule and erg respectively.

Work done – example problems:

Problem 1> 5 N force is applied on a cube and moves 8 m along the direction of a force. What amount of work is done on the cube?

Problem 2> 50 N forces making an angle 60° applied on an object. Calculate the amount of work done.

Please comment on your answers below.

What is Energy in Physics?

Capacity of doing work by an object is known as energy.

The unit of energy and work done is the same. SI unit of energy is Joule (J) and c.g.s unit of energy is erg. More units of Energy here.

1 joule = 107 erg.

Forms of Energy

Energy can be classified into 8 types.

Mechanical energy: Mechanical energy arises on an object due to the motion or rest (not absolute rest). There are two types of mechanical energy. One is kinetic energy and the other is potential energy.

> Kinetic energy: When an object is in motion with respect to another object, it constitutes mechanical energy. A particle moving with constant velocity, v, it’s kinetic energy will be (1/2)mv2, where m is the mass of an object.

Formula of kinetic energy Ek = (1/2)mv2

 > Potential Energy: Capacity of doing work developed in a body due to its position or configuration is called its potential energy (PE). PE arises when a body is confined to a force field. As an example, when a body of mass, m kept at a height, h from the earth surface, it constitutes mgh amount of energy in the body.

Formula of potential energy Ep = mgh. where g = gravitational acceleration.

Electrical Energy: Electrical energy stored in the electric field produced by a charged particle around it. This energy derived charged particles from power stations to our home supplying electric current. Every day we used electric energy for our daily life. Electric bulb, fan, computer, air conditioner, etc use electric energy.

Electric Energy density, Uelc = (1/2)μE2 ; μ = permittivity; E = electric field

Magnetic Energy: Magnetic energy stored in the magnetic field produced by the magnet. When an iron’s pin is kept near to a magnet, the magnet attracts it. Why? Because the field stored some amount of energy that helps to attract the iron’s pin towards the magnet. A big bar magnet exists inside the earth.

Magnetic Energy density, Umeg = (1/2)εB2 ; ε = permeability and B = magnetic field

From electrodynamics, we know that a changing magnetic field produces an electric field and a changing electric field produces a magnetic field.

Chemical Energy: In a molecule, atoms are closely held together. How the atoms are bonded? Energy called chemical energy helps to create such a bond that helps atoms to hold close and form a molecule. Thus Chemical energy is defined as the energy stored in the bonds of chemical compounds. When water is mixed with lime, the heat produced. The chemical energy stored in the lime comes out as heat energy. A dry cell uses its chemical energy to produce electric energy.

Light Energy: Energy stored in the light is called light energy. Green plants use light energy in the photosynthesis process to stored light energy into chemical energy inside glucose. A solar cell uses solar energy to produce an electric current.

Sound Energy: Energy stored in the sound is called sound energy. When we speak, our vocal cord vibrates and energy flows as a sound wave. When we stand near to a big DJ speaker our clothes start to vibrate. Why does it happen? Because sound energy is responsible for creating such vibration.

Nuclear Energy: Energy stored in the nucleus of atoms is nuclear energy. Protons are positively charged. The same charges repel each other. In the nucleus of atom protons also repel each other. So the nucleus must not exist. But in nucleus protons are held together. Who is responsible to hold protons together in the nucleus? The answer is nuclear energy, which strongly holds all the particles inside the nucleus of atoms. We can exert nuclear energy from the nucleus of Uranium or Thorium in the nuclear power plant. In an atom bomb, a huge amount of nuclear energy releases when it blasts.

Gravitational Energy: The energy stored in the gravitational field is called gravitational energy. When we lift some object up, gravitational energy starts to store in the object as potential energy. Due to gravitational energy, all the objects having mass in the universe attract each other. Sun attracts earth, or earth attracts the moon due to gravitational energy stored in the gravity or gravitational field.

What Is Power in Physics?

The definition of work says nothing about the time during which work is done. Suppose you move at a distance by walking or running. But you feel more tiredness when you run. Both cases work is done by the same amount. Then why we get tired in the case of running. The answer is given by introducing power. In the case of running, you required more power and hence you get tired. Another example of power is – a strong boy can lift up 100 kg weight but weak boy can not. Because a strong boy can generate more power to lift the weight up than weak boy.. Power is a physical quantity which is defined as follows.

Rate of doing work is known as power. Simply rate of change of work done with respect to time is called power.

Thus Power, P = (Work done)/Time = W/t.

Power is a scalar quantity. Its SI unit is Watt. 1 watt = 1 Joule/second. In so-called machinery system unit of work is Horse Power (HP).

1 HP = 746 watt.

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Newton's Laws of Motion, Momentum Force General Knowledge

Newton’s Laws of Motion, Momentum Force > Important Physics GK [PDF]

Newton’s Laws of Motion, Momentum Force General Knowledge

Newton’s Laws of Motion, Momentum Force related GK for you competitive examinations such as UPSC, IAS, Civil Service, Staff Selection Commission or SSC, CGL, MTS, Banking SBI PO, Railway, etc. Dear aspirants, read this topic carefully. This is an important part of physics from which some questions may be listed on your question paper.

Contents

Newton’s Laws of Motion
Newton’s First law of motion
Definition of Force
Inertia
Momentum
Newton’s Second Law of Motion
Newton’s Third Law of Motion
Moment of Force

To describe the characteristics of motion we need to set up some laws, which enable us to understand or explain the motion of a particle. There are three fundamental laws provided by English physicist Sir Isaac Newton. He is the father of physics. He first established his three laws of motion in his book ‘Principia‘. According to his name, three laws are named Newton’s First Law, Newton’s Second Law, and Newton’s Third Law.

In this chapter, we will first state the laws of motions than we well elaborate briefly. We will also see how force is defined from the first law as well as how it is measured from his second law.

Newton’s Laws of Motion:

Newtons First Law:

Every object continues in its state of rest or of uniform motion in a straight line if no net force acts upon it. This is also known as law of inertia.

Explanation: Let us consider a particle moves in a straight line. According to the first law, the speed and direction will remain the same unless the object faces an external force. Here external force means the force applied on the object from outside. But wait, when we through a ball with an initial speed, its speed continues to decrease until it comes to rest. Here we do not apply any external force, then why it stops after traveling some distance? Well, though we do not exert any force from outside, a frictional force by air or ground comes to act on the ball. This friction is the cause to stop the ball from moving with constant speed in a straight line. This friction opposes the constant motion of the particle.


Definition of force from First Law: From first law, we see that we need to apply an external force to change its motion. Thus force may be defined as follows. What we apply from outside to change the motion or to change the shape, size or direction of an object is called force. Therefore force can change the velocity, shape or size of an object. SI unit of force is Newton. In c.g.s system unit of force is dyne. When frictional force applies to move the ball, it decreases the speed of the ball.

1 Newton force = 105 dyne.


Inertia from First Law:

Inertia is a property of a body by virtue of which the body opposes a change in its initial state of rest or motion along a straight line. First law state that the motion of a body never changes unless the application of force. Thus if a body is in rest it tries to stay rest and if the body is in motion it tries to be in motion forever.

There are two types of inertia –

  1. Inertia of rest
  2. Inertia of motion

Inertia of rest: Inertia of rest means the body tries to stay in its rest state forever. Example: When a car or train starts moving suddenly the passengers bend backward. This is because when the train or bus moves suddenly our lower part of the body start to move i,e, become dynamic but our upper part of the body remains to its original static or rest state.

Inertia of motion: Inertia of motion means the body tries to stay in motion forever. Example: When a car or train stops suddenly we bend forward. Similarly, in this case, our lower part of the body become rest as the train or bus stop but our upper part tries to maintain its original motion.

To state the second law of motion we first need to introduce another physical quantity, momentum.

Momentum: In physics, momentum is defined as the product of mass and velocity. It is a vector quantity as velocity is. SI unit of momentum is Kilogram-meter/second or Kg-m/s.

Thus Momentum p = m*v,

m = Mass of object and v = velocity.

Now understand what actually momentum is. Let an empty truck (less mass) moving with greater velocity than a loaded truck (with greater mass) moving with less velocity. If both trucks collide a wall, which truck will dismantle the wall more? If we take into account mass and velocity individually, it is hard to answer the question. Because it does not mean that more mass with less velocity will produce more damage than less mass with more velocity and vice versa. Thus another physical quantity is needed to introduce to explain this phenomenon. Momentum is a new kind of physical property of matter that arises when an object has some velocity and mass. Therefore multiplying mass by velocity, we can measure momentum.

Newton’s Second Law

The rate of change of momentum is directly proportional to the applied force on the body and takes place in the direction of force.

I have already told you that the second law gives us the magnitude of the force. Now let us see how to deduce the formula of force.

newton's second law of motion mathematical formula

Consider a particle of mass 'm' having initial velocity 'v1. After some time 't' velocity become v2. Then initial momentum is mv1 and final momentum is mv2.

Change of momentum Δp =  mv2 −  mv1

Rate of change of momentum, Δp/t = (mv2 −  mv1)/t

According to second law, Force ∞ Δp/

or, F ∞ (mv2 −  mv1)/t

or, F = k*(mv2 −  mv1)/, [Where 'k' = proportional constant;]

or F = k*m*(v2 −  v1)/t

or F = k*m* a; [Where a =  acceleration = (v2 −  v1)/t]

According to definition of 1 N force (to produce unit acceleration on unit mass, force required is one Newton) if mass is 1 kg, acceleration is 1 m/s2, and force is 1 N then the constant 'k' is 1.

Thus F = ma

This is the equation of force deduced from the second law of motion.

Newton’s Third law:

Newton’s third law is stated as “every action there is an equal and opposite reaction”.

The statement means that body A exerts a force on body B, then an equal and opposite force will also exert on body A by body B. Example: Suppose a gun fire a bullet. The gun exerts a force on bullet. According to the third law, the bullet also exerts opposite and equal force on the gun. That’s why when the bullet is fired, the gun experience recoil in the backward direction.

Newton's third law

Other good examples of Newton’s third law are rocket propulsion and a jet engine. The rocket contains solid fuel. Fuel burns and hot gasses propels out with very high velocity. This is an action. So the reaction of this force propels the rocket forward.

Impulse: Impulse is defined as the product of Force and time. Impulse is a vector quantity and its direction is along the direction of the force.

Force F * Time t = Impulse = Change in momentum.

If the time of contact of two moving bodies is small then a large change of momentum occurs producing a large impact of force.

Centripetal force: It is an external force that required maintaining the circular motion of a body. When a body moves circularly, its direction, as well as velocity, always changes. Therefore to changing velocity produces a change of momentum. According to the second law changing momentum gives us force. When an object rotates it always constitutes a centripetal force that acts along the center of curvature.

Centripetal centrifugal force

Centrifugal force: It is a Pseudo force and equal and opposite to centripetal force.

Moment of Force: Moment of force is an effect of rotation. The turning effect of an object about a point or an axis of rotation is known as a moment of force. In our daily life, we utilize the rotational effect. As an example, when we try to open a door by pushing nearer to hinges, a larger force is required. Thus rotational effects depend on two factors –

  1. How much force is applied i.e. magnitude of force;
  2. And the distance of force from the axis.

moment of force

More the distance from the rotational axis less force is required. Thus the moment of force is mathematically described as the product of the magnitude of the force and the distance between the point on which force is applied and rotational axis.

Read: Gravitation – Physics > GK

Thus Moment of force = force × perpendicular distance;

It is a vector quantity. SI unit is Newton-meter (N-m).

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Motion – Its Equations gk

Motion – Its Equations > Important Physics GK [PDF]

Motion in Physics General Knowledge

Motion in Physics General Knowledge for UPSC, IAS, Railway, Banking, SSC, CGL, MTS, and other competitive govt. job examinations. Motion and its equations are very important and I am sure some of the questions from this topic will come in the above exams. So read this topic carefully.

Mechanics is a branch of physics. In this branch of physics, we deal with the motion of an object.

Contents:

What is motion in physics
Type of motion
Equations of Motion (Linear)
Circular Motion

What is motion in physics?

When an object changes its position with respect to time, we can say, the object is in motion. Or in other words, as time goes on, the body or object moves from one particular position to another.

Type of motion:

Mechanical motion can be classified into two types, –

Translational or Linear Motion: In Translational motion, an object moves linearly. Example: If a car moves on the road, its motion is translational.

Rotational Motion: In rotational motion, an object rotates or spins about a fixed point or an axis. Example: Moving of top about its axis, moving earth around the sun, etc are examples of rotational motion.

To explain or understand the motion of an object we need to introduce some physical quantities, like distance, displacement, speed, velocity, acceleration, momentum, etc are required to explain the linear motion. And angular velocity, angular acceleration, etc are required to explain rotational motion. Note that for both kinds of motion, time is necessary. Now let us define each physical quantity briefly.

Distance: Distance is the length of the actual path covered by an object which is in motion in some interval of time. Distance is a scalar quantity as it has no particular direction.

Let us consider an object moves 5 m along the north, then it goes to 6 meters along the east and again goes to 8 m along the south. The total distance covered by the object is (5+6+8) m = 19 m.

Displacement: Displacement is defined as the shortest distance covered by a moving object in a particular direction in a given interval of time. Displacement is a vector quantity as it has a particular direction i,e, displacement take into the direction also.

Distance vs Displacement

If an object goes 3 m in the north (AB) and then 4 m in the east (BC), then its Displacement will be the distance from the starting point to endpoint i,e shortest distance between two points. In this case, the distance is simply (3+4) m = 7 m, but its displacement will be √(32+42) = 5 m along AC. Both distance and displacement have the same unit i.e. meter in the SI system. Another important thing to remember is that the displacement may be positive, negative or zero, but the distance is always a positive quantity. Thus magnitude of displacement ≤ distance as usual.

Speed: Speed is defined as the distance travel by an object in a unit interval of time. Speed is a scalar quantity as the distance is. Generally, speed is denoted by ‘s’. In the SI system, the unit of speed is meter/second.

Thus Speed = (distance)/(time) or s = d/t.

Suppose an object move 50 m distance in 10 seconds. Its speed is 50/10 = 5 m/s

Velocity: Displacement per unit time is called velocity. Velocity is a vector quantity because displacement is vector ( If we divide or multiply a vector by scalar we get vector). The unit of velocity is the same as speed i.e meter/second (m/s). Usually, velocity is denoted by ‘v‘. (Bold text v to denote vector).

Thus, Velocity = (Displacement)/ Time. Or v=D/t

From the above figure, displacement is 5 m along AC. Now this displacement covered by the object in 2 seconds, then its velocity will be (5/2) = 2.5 m/s.

Acceleration: The rate of change of velocity i,e velocity change per unit time is called acceleration. Acceleration is a vector quantity. Its SI unit is meter/(second)2.  Thus

Acceleration = Velocity/time. or a=v/t.

Now consider an example. Initial velocity (v1) of a car is 4 m/salong north. After 5 second it final velocity (v2) is 19 m/s2. Then,

Acceleration a = (v2 – v1)/5 = (19-4)/5 = 15/5 = 3 m/salong north.

Acceleration due to gravity: One of the most familiar acceleration is due to gravity. If we drop some object from a height it does not fall with a uniform velocity. Initially, its velocity is zero. As long as it goes to down its velocity continuously or uniformly increases. This is because earth exerts a gravitational force on the object and subsequently its velocity increases uniformly producing acceleration. The magnitude of gravitational acceleration (g) of the earth is 9.8 m/s2.

Equations of Motion (Linear):

Equations of motion are very useful in solving problems. Let displacement, initial velocity, final velocity, acceleration and time are denoted by S, v, u, a ,and t respectively, then the following equations of motion are very important to solve problems.

Equation-1> v = u + at

Equation-2> S = ut + (1/2)*at2

Equation-3> v2 = u2 + 2aS.

Circular Motion:

When an object moves around a point in a circular path, its motion is called circular motion. In a circular motion, the direction of object changes continuously constitutes an acceleration. Thus circular motion always has acceleration. If the object moves circularly with the constant speed it constitutes an angular velocity, which is always a vector quantity. If it rotates anticlockwise, the direction of angular velocity is upward.

Angular velocity: When an object rotates it always subtended an angle ‘θ’. The rate of change of angle with respect to time is called angular velocity. It is denoted by ‘ω’.

Angle and Angular velocity

Thus Angular velocity = angle/time or ω = θ/t.

Time Period: Time Period is defined as the time taken to complete one revolution or one oscillation. It is denoted by ‘T’. It is a scalar quantity.

Frequency: The number of complete oscillations or complete revolution per unit time is called frequency. It is denoted by ‘ν’ and the SI unit of frequency is Hertz (Hz).

The relation between time period and frequency:

T = 1/ν

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Physical quantities standard and units in physics general knowledge

Physical Quantities Measurements Standards & Units > Important Physics GK [PDF]

Physical Quantities, Measurements Standard and Units GK

Physical quantities, Measurements standard and units general knowledge (general science gs) for UPSC, IAS, Banking, Railway SSC and other competitive examinations.

Contents:
Physical Quantities
Standard and Units
Physical Quantities With Their Symbols And Units in SI & c.g.s System

To explain the natural phenomena we take the help of physics. Physics enable us to understand logically as well as mathematically all natural phenomena. That’s why we introduced the Physical quantity and unit.

Physical Quantities

All the laws of physics are generally expressed in terms of Physical Quantities. As an example, if you go to school or college from your home by walk, you need to know your speed and time. If you start to go at 9:30 AM and reach at 10 AM, you spend 30 minutes by walk. Again distance between your school and home is 6 Km then you can easily calculate your walking speed which is [Distance/Time] =  200m/minute. Thus from the above example, time, speed and distance are Physical Quantities. Some other kinds of physical quantities are force, momentum, temperature, density, area, pressure, acceleration, etc.

We need to measure the physical quantities to obtain physically meaningful results to understand physics. So measurement is necessary for physics.

Classification of Physical Quantities:

Generally, Physical Quantities are classified into two classes such as fundamental and derived quantities.

Fundamental Quantities: They are not defined in terms of other physical quantities. Example: Length, Mass and Time.

Derived Quantities: Their definition derived from mainly fundamental physical quantities. Example: speed, area, acceleration, momentum, density, etc. In case of speed to define it, you need to two fundamental quantities like Length and time.

Classification of Physical quantities in terms of Direction:

Physical quantities are also classified into two types one is Scalar and the other is Vector quantity.

Scalar Quantity: Physical quantities that have the only magnitude NOT direction. Speed, density, mass, work, energy, power, etc are scalar.

Vector Quantity: A vector quantity is one that has BOTH magnitude and direction. Force, momentum, displacement, acceleration, velocity, etc are vector quantities.

Explanation: Vector quantities are denoted by putting a ‘bar’ (—) or ‘arrow’ (→) sign. Like force is a vector quantity and denoted by –

Now if you push a table along north direction by applying force 5 Newton, then according to vector rule, it is written as 5N-North.  Here 5 is a scalar and if you put its direction (here North), it becomes a vector.

Standard and Unit:

To measure the physical quantities we need to introduce standards and units. Measurement of physical quantities consists of two steps –

  1. one is a choice of the standard and
  2. the other is a comparison of the standard to the quantity to be measured.

Here the choice of the standard is known as Unit. A comparison of the standard to the quantity to be measured provides the total measurement of that quantity. Consider the length of a pen, it is about 10 cm long. It means that the pen’s length is 10 times the unit of length, centimeter.

Units depend on choice. Each choice of units leads to a new system or set of units. You may consider any length as a unit of length. But it is not standard. Earlier, people from various countries used different systems of units. In the year 1960 GCWM recommended that a metric system of measurements called the International System of Units or SI Unit (System Internationale).

Classification of Units:

Units are also classified into two types

Fundamental Units: can not be derived from other unit. Three fundamental units are Meter, Kilogram and Second.

Basic UnitsThere are seven basic units – meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mol, Candela (Cd).

Supplementary unitsPlane angle and Solid angle are considered as Supplementary units.

Derived Units: can be derived from other units.

Unit of Length: In SI system the unit of length is meter. One meter is defined as the distance between two lines on a particular platinum-iridium rod at 0° C. This rod is kept in the IOWM office located near Paris. In modern physics, it is also defined as the path travel by light in free space during a time interval of 1/299792458 second. In c.g.s and fps system, the unit of length is centimeter and foot respectively. For the large distance, we used Kilometer, Mega meter mile, etc. To measure the distance in space we used the astronomical unit or AU, light-year, and parsec. 1 AU is the distance between earth and sun.

1 parsec = 3.2615 light-years = 206264.8 AU = 3.085×1016 m.
1 Light-year = 63241.1 AU = 9.461 trillion km = 9460730472580800 m.
1 AU = 149597870 km. = 149597870700 m.
1 km = 1000 m. = 10m = 105 cm.
1 m = 100 cm.

Similarly, a very small distance is measured by millimeter (mm), micrometer (μm), angstrom (Å), nanometer (nm) and femtometer (fm).

1 m = 106 μm = 109 nm = 1010 Å = 1015 fm.

Units are also classified into various types such as C.G.S, M.K.S, F.P.S, etc. CGS is for a small unit and mks are for larger.

Unit of Mass: In SI system the unit of mass is Kilogram (Kg). One kg is defined as the mass of a particular solid cylinder of platinum-iridium alloy kept at Sevres. To measure the large masses we used tonne. In c.g.s and f.p.s system, the unit of mass is gram and pound respectively.

1 tonne is equal to 103 kg.

Unit of Time: In SI system the unit of time is second. It is represented by small later “s”. Previously it was defined as the 1/86400th part of a mean solar day. But in modern physics, 1 second is redefined as atomic clock such as time is taken to complete 9192631770 periods of transition of the two hyper levels of the ground state of the Caesium 133 atom.

Physical Quantities With Their Symbols And Units in SI & c.g.s System

 Physical
Quantity
 Symbol* Unit in SI SI Unit
Symbol
 Unit
in c.g.s
  c.g.s Unit
Symbol
 Length l Meter m Centimeter cm
 Mass M Kilogram kg gram g
 time t Second s second s
 electric
current
 I ampere A biot biot
 temperature T kelvin K kelvin K
 amount of
substance
 n Mole mol  
 luminous
intensity
 Iv Candela Cd  
 area A square metre m2 square
centimeter
 cm2
 volume V Cubic meter m3 Cubic
centimeter
 cm3
 speed,
velocity
 v, s meter/second m/s cm/second cm/sec
 acceleration a meter/second2 m/s2 cm/second2 cm/s2
 Angular
momentum
 L kg-m2/s  g-cm2/s 
 Angular
speed
(or angular
velocity)
 ω rad s−1 – rad s−1 –
 Capacitance C Farad F statfarad statF
 wavenumber k reciprocal metre m-1 reciprocal cm cm-1
 Current
density
 J ampere/meter2 A/m2  
 density,
mass density
 ρ kg/cubic metre kg/m3 gram/metre3 g/m3
 Electric
charge
 Q coulomb C statcoulomb e.s.u
 Electric
potential
 V Volt V statVolt statV
 Electrical
resistance
 R ohm Ω – –
 Energy E Joule j Erg erg
 Force F Newton N Dyne dyn
 Frequency f Hertz Hz Cycle/sec 
 magnetic
field
 B tesla tesla gauss gauss
 refractive
index
 μ unit less – unit less –
 Inductance L henry H abhenry abH
 Momentum p kg-m/s kg-m/s g-m/s g-m/s
 Permeability μ henry/meter H m−1 abhenry/cm abH/cm
 Permittivity ε farad/meter C2N-1m-2  
 plane angle Θ radian rad – –
 solid angle Ω steradian sr – –
 pressure P pascal (N/m2) Pa bar Dyne/cm2
 power P watt or
(Joule / second)
 W Erg/second 
 Specific
heat capacity
 c J kg−1 K−1   
 Wavelength λ Meter m Centimeter cm
 Entropy S Joule/Kelvin J K−1 – –
 dynamic
viscosity
  Pascal-second Pa·spoise or
[g/(cm·s)]
 P
 Heat Q Joul J Erg erg
 Surface
tension
 Y N m−1 or J m−2  Dyn cm−1/erg m−2 
 Chemical
potential
 μ Joule/ mol J mol−1  

* The bolt symbols represent vector quantities.

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