• MEASUREMENT TECHNIQUES:

1. Systematic Error: A constant or consistent error in measurement which may be attributed to a fault in the instrument or a consistent flaw in the measuring technique, and which cannot be eliminated by averaging.

2. Random Error: An error of variable magnitude in which the readings are scattered about the true value. This type of error is due to limitations on the part of the observer or an inconsistency in measuring equipment. It can be eliminated by averaging.

3. Precision: The degree of refinement with which an operation is performed or a measurement is stated. It relates to how close measurements are to their mean value.

4. Accuracy: The degree of conformity of a measure to a standard or a true value. • PHYSICAL QUANTITIES & UNITS:

1. Principle of Homogeneity: states that in a homogenous equation, every expression, on either

side of the equation, has the same dimensions.

2. Homogenous Equation: An equation in which the base units of all quantities added or subtracted is the same on either side of the equation.

3. Physical Quantity: A quantity that has dimension and can be measured.

4. Scalar Quantity: A quantity in which only the magnitude is of significance and does not possess directional properties.

5. Vector Quantity: A quantity possessing both a magnitude and direction.

6. Base Unit: The units for the seven basic physical quantities. The following are the seven basic quantities with their respective units:

Basic SI Units

Properties Units Mass kg [Kilogram]

Length m [Meter] Time s [Second

Electric Current A [Ampere] Temperature K [Kelvin]

Intensity of Light Cd [Candela] Amount of Substance mol [Mole]

Prefixes

Prefix Symbol Prefix Name Value P Peta T Tera G Giga M Mega k Kilo d Deci c Centi m Milli µ Micro n Nano p Pico f Femto A Atto

• KINEMATICS:

1. Distance: The length of the path between two points. It is a scalar quantity and is measured in

the SI unit meter (m).

2. Displacement: The shortest distance between two points in a linear direction from a fixed point of reference. It is a vector quantity measured in the SI unit meter (m).

3. Speed: The rate of change of distance. It has the formula and is a scalar quantity measured in the SI unit meter per second (ms-1).

4. Velocity: The rate of change of displacement. It has the formula and is a vector quantity measured in the SI unit meter per second (ms-1).

5. Acceleration: The rate of change of velocity. It has the formula and is a vector quantity measured in the SI unit meter per second square (ms-2).

Kinematics

Formula to determine acceleration of free fall (i.e. gravity)

• DYNAMICS:

1. Newton’s First Law: A body continues in a state of rest or of motion at a constant speed in a straight line unless acted upon by an external force.

2. Newton’s Second Law: The net force acting on a body of constant mass is directly proportional to the acceleration it gains if no external force is acting on the body. Fnet = ma.

3. Newton’s Third Law: For every action, there is an equal but opposite reaction.

4. Mass: The measure of a body’s resistance to changes in its dynamic state. It is a scalar quantity measured in the SI unit kilogram (kg).

5. Weight: The force a body experiences due to the effect of gravitational acceleration on its mass towards the centre of the earth. It has the formula W = mg and is a vector quantity measured in the special SI unit Newton (N).

6. Linear Momentum: The product of the mass of a body and its velocity. It is a quantity that describes the motion of a body. It has the formula p = mv and is a vector quantity measured in the SI unit Newton second (Ns).

7. Force: The rate of change of momentum of the body upon which it acts. It has the equation F = dp/dt and is a vector quantity measured in the SI unit Newton (N).

8. Principle of Conservation of Momentum: The total momentum of interacting bodies in a closed system remains constant providing that there is no external force acting on it.

9. Elastic Collision: A collision in which kinetic energy, linear momentum and the total amount of energy are all conserved.

10. Inelastic Collision: A collision in which the bodies coalesce upon impact. The kinetic energy is not conserved but the total amount of energy and linear momentum is conserved.

11. Perfectly Elastic collision: A collision in which the masses of the two bodies colliding are equal and the two bodies interchange their velocities after collision. Kinetic energy, linear momentum and the total amount of energy are all conserved.

x

20N

30°

y

Dynamics

Rule:

Law of Conservation of Momentum: i.e.

i.e. Relative velocity of approach = relative velocity of separation

• FORCES:

1. Up thrust: The buoyancy force acting upwards on an object when it is completely or partially immersed in a fluid resulting in apparent loss in weight. The magnitude of the up thrust is equal to the weight of the fluid displaced. It has the formula U = weight of fluid displaced and is a vector quantity measured in the SI unit Newton (N).

2. Centre of Mass: The point where the mass of an object may be assumed to be concentrated. If a force is applied through this point, the body translates and does not rotate.

3. Centre of Gravity: The point through which the weight of a body may be assumed to act. It has a symbol (G).

4. Couple: Two forces of the same magnitude, parallel to each other, acting in opposite directions on the same body, but not along the same line, which tend to rotate the body on which they are acting.

5. Moment of a Force: The product of the force and the perpendicular distance between the line of action of the force and the pivot. It has the formula ‘moment = F x d’ and is a pseudo-vector quantity measured in the SI unit Newton meter (Nm).

6. Moment arm: The perpendicular distance between the line of action of a force and the pivot. It is measured in the SI unit meter (m).

7. Torque of a Couple: The net moment produced by a couple. Its magnitude is the product of one of the forces and the perpendicular distance between the couple. It has the formula T=fd and is a pseudo-vector quantity measured in the SI unit Newton meter (Nm).

8. Principle of Moments: For a body/system in equilibrium, the sum of the clockwise and anticlockwise moments about any point in or out of the system is equal.

9. System in Equilibrium: A system is said to be in equilibrium when the net force in any two perpendicularly resolved directions is individually equal to zero, or when the sum of the moments about any point in or out of the system is equal to zero.

10. Centripetal Force: The force that is necessary to keep an object moving in a circular path and that is directed inward towards the centre of rotation.

Pressure

In fluids,

Up thrust

i.e. force acting upwards on the bottom surface

i.e. pressure acting downwards on the upper surface

i.e. force acting downwards on the upper surface

Density =d Area = A Height = x Mass = dAx Weight = mg = dAxg

Volume = Ax

For flotation:

Moment

, where ‘d’ is the perpendicular distance between the line of action of the force and the pivot.

, where ‘d’ is the perpendicular distance between the two forces constituting the couple.

• WORK, ENERGY & POWER:

1. Principle of Conservation of Energy: The total amount of energy within a closed system remains constant, i.e. energy can neither be created nor destroyed, but can be changed from one form to another with the total amount remaining constant.

2. Work: The product of the force and the displacement in the direction of the force. It has the formula W=Fs and is a scalar quantity measured in the SI unit Newton meter (Nm), or joule (J).

3. Gravitational Potential Energy: The energy possessed by a body, available to do work, due to its height above a reference point. It has the formula EG.P. = mgh and is a scalar quantity measured in the SI unit joule (J).

4. Electric Potential Energy: The energy possessed by a charged body, available to do work, due to its position in an electric field. It has the formula EE.P. = QV and is a scalar quantity measured in the SI unit joule (J).

5. Elastic Potential Energy: The energy that is stored in a body due to its deformed (i.e. stretched or compressed) condition, and is available to do work. It has the formula EE.P = ½Fe or EE.P = ½ke² and is a scalar quantity measured in the SI unit joule (J).

6. Potential Energy: The stored energy in a body available to do work. It is a scalar quantity measured in the SI unit joule (J).

7. Kinetic Energy: The energy possessed by a body, available to do work, due to virtue of its motion. It has the formula EK=½mv2 and is a scalar quantity measured in the SI unit joule (J).

8. Internal Energy: The sum total of the random kinetic and potential energies of the atoms or molecules of a substance.

9. Efficiency: The ratio of the useful work done to the total input energy. It has the formula η = useful work done ÷ total input energy or η = useful power output ÷ total power input, and is a scalar quantity with no units. Percentage efficiency can be calculated by multiplying the efficiency by 100.

10. Power: The rate at which work is done. It has the formula P=work done ÷ time taken and is a scalar quantity measured in the SI unit watt (W).

Energy

, where ‘Q’ represents heat energy, ‘m’ represents mass, ‘c’ represents specific heat capacity, and ‘θ’ represents the change in temperature in degrees Kelvin or degrees Celsius.

In gases,

Power

, where ‘F’ represents force, and ‘v’ represents velocity.

• NUCLEAR PHYSICS:

1. Nucleon Number (A): The total number of protons and neutrons in a nucleus.

2. Proton Number (Z): The total number of protons in a nucleus.

3. Nuclide: A species of atom characterized by the constitution of its nucleus and hence by the number of protons, the number of neutrons, and the energy content.

4. Isotope: Different forms of the same element with the same number of protons but different number of neutrons.

5. Nuclear Decay: The process in which unstable nuclei disintegrate and emit α-particles, β- particles and/or γ-rays in the process.

6. Spontaneous Decay: Decay that is unaffected by environmental changes such as temperature, pressure or humidity.

7. Random Decay: All identical nuclei have an equal probability of decay in a given time interval but is not possible to predict when an individual nucleus will decay.

8. Alpha-Decay: A type of nuclear decay in which the mass number decreases by 4 units while the atomic number decreases by 2 units as an α-particle is emitted from the nucleus.

9. Beta-Decay: A type of nuclear decay in which a high-speed electron (a β-particle) is emitted from the nucleus resulting in an increase in the atomic number by 1 unit and no change in the mass number.

10. Radiation: A type of nuclear decay in which γ-rays are emitted from the nucleus and there is no change in either the atomic number or the mass number.

Radioactivity

Alpha-decay Equation

Beta-decay Equation

• CURRENT ELECTRICITY:

1. Electric Current: The rate of flow of charge. It is given by the formula I=dQ/dt and is a scalar quantity measured in the SI unit ampere (A). Conventionally the direction of current is taken to be in the direction of flow of positive charge.

2. Charge: Charge is defined as the product of current and time. It is a scalar quantity measured in coulombs (C).

3. Coulomb: A unit of electric charge equal to the quantity of electricity transferred by a current of one ampere in one second. One coulomb consists of 6.25×1018 electrons.

4. Volt: A unit of electrical potential difference and electromotive force equal to the potential difference between two points in a conducting wire carrying a constant current of one ampere when the power dissipated between these two points is equal to one watt, or the potential difference between two points in a circuit if one joule of energy is dissipated between the two points when one coulomb of charge flows between the two points.

5. Resistance: The ratio of the potential difference across the ends of a load to the current flowing through it. It is given by the formula R=V/I and is a scalar quantity measured in the SI unit ohm (Ω).

6. Internal Resistance: The resistance to the flow of current a cell or a battery offers before the current is supplied to the external circuit.

7. Ohm: A unit of electric resistance equal to the resistance of a conductor in which a potential difference of one volt produces a current of one ampere.

8. Ohm’s Law: The potential difference across a component is proportional to the current flowing through it providing physical conditions remain constant. It is represented by the formula V=IR.

9. E.M.F: The electromotive force of a source is defined as the energy supplied per unit charge by the source to drive the charge round a complete circuit including the internal battery. The

e.m.f. represents the conversion of chemical energy to electrical energy. It is given by the formula E = energy converted ÷ total charge and is a scalar quantity measured in the SI unit volt (V).

10. P.D.: The potential difference between two points is defined as the energy expended per unit charge when the charge flows from one point to another. The p.d. represents the conversion of electrical energy into other forms of energy such as thermal energy. It is given by the formula E = energy converted ÷ total charge and is a scalar quantity measured in the SI unit volt (V).

• D.C. CIRCUITS:

1. Kirchoff’s First Law: The sum of the currents entering a node in a circuit is equal to the sum of the currents leaving the node. This results from the conservation of charge.

2. Kirchoff’s Second Law: For a closed circuit, the algebraic sum of the e.m.f.s is equal to the algebraic sum of the product of the currents and resistances in the circuit. This results from the conservation of energy.

Electricity

[Kirchoff’s Current Law]

[Kirchoff’s Voltage Law]

• ELECTRIC FIELDS:

1. Electric Field: An area or region in which a charged particle experiences a force.

2. Electric Field Strength: The force experienced per unit positive charge when placed in an electric field. It is given by the formula E=F/Q or E=V/d and is a vector quantity measured in the SI units Newton per coulomb (NC-1) or volts per meter (Vm-1).

Electric Fields

• PHASES OF MATTER:

1. Density: The mass per unit volume of a body. It has the formula ρ = m/v and is a scalar quantity measured in the SI unit kilograms per meter cube (kgm-3).

2. Crystalline solids: They possess a lattice structure in which particles are arranged in a regular, fixed and repetitive manner, three-dimensionally, over a large distance. They are generally formed on slow cooling of a liquid to the solid state as the particles have time to arrange themselves in an orderly manner.

3. Metals: They possess a poly-crystalline structure consisting of a ‘sea’ of delocalised electrons surrounding the positive metal ions arranged in a regular pattern. They consist of a lattice in which there is long-range order and the atoms are arranged in a repetitive pattern within the structure

4. Polymers: The structure consists of long chains of molecules, often containing as many as 10 000 smaller units called monomers arranged repetitively. Cross-links may exist between molecules and the structure may be classified as either amorphous or crystalline depending on the order of arrangement.

5. Amorphous Materials: They do not possess repeated and closely-packed structures over a long-range, but rather possess short-range structures. Amorphous solids are formed on rapid cooling of a liquid as this does not give sufficient time for the particles to arrange themselves in an orderly manner. They do not possess fixed melting points.

6. Liquid: A fluid that has no independent shape but has a definite volume, does not expand indefinitely and is only slightly compressible.

7. Solid: A substance that does not flow perceptibly under moderate stress, has a definite capacity for resisting forces (compression or tension) which tend to deform it, and under ordinary conditions retains a definite size and shape.

8. Gas: A fluid that has neither independent shape nor volume but tends to expand indefinitely.

9. Pressure: The force acting per unit area. It has the formula P = F/A and is a scalar quantity measured in the SI units Newton per meter square (Nm-2) or Pascal (Pa).

10. Melting: The change of state from a solid to a liquid with the absorption of latent heat of fusion, without a change in temperature. This occurs at a specific temperature, known as the melting point, for a pure substance.

11. Boiling: The change of state from a liquid to a gas with the absorption of latent heat of vaporisation, without a change in temperature. This occurs at a specific temperature, known as the boiling point, for a pure substance.

12. Evaporation: The process in which more energetic particles leave the surface of a liquid as vapour. This can occur at any temperature.

13. Brownian Motion: The erratic, unpredictable and continuous random movement of microscopic particles suspended in liquids or gases resulting from the impact of molecules of the fluid surrounding the particles.

• DEFORMATION OF SOLIDS:

1. Stress: The force applied per unit area of cross-section, it has the formula σ = F/A. It is a scalar quantity measured in the SI unit Pascal (Pa).

2. Strain: The extension per unit length. It has the formula ε = ∆l/l and is a scalar quantity with no units.

3. Young Modulus: It is the property of a material that measures the stiffness of a body and is defined as the ratio of stress to strain within the limit of proportionality for a material. It has the formula E=Fl/A∆l and is a scalar quantity measured in the SI unit Pascal (Pa).

4. Elastic Deformation: Elastic deformation has occurred when a material returns to its original length and all the work done in deforming the material can be recovered on removal of the deforming forces acting on the material.

5. Plastic Deformation: Plastic deformation has occurred when there is some permanent extension in a material and all the work done in stretching the material is not recovered after the removal of the deforming forces acting on the material.

6. Elastic Limit: The elastic limit of a material is the maximum length by which it can be deformed and still regain its original shape after the deforming forces are removed.

7. Hooke’s Law: The force applied to a body is directly proportional to the extension in the material provided that the limit of proportionality is not exceeded. It is represented by the formula F = ke.

8. Spring Constant: It is the amount of force required to produce unit extension in a material. It is a scalar quantity and has the SI unit Newton per meter (Nm-1).

9. Ultimate Tensile Stress: The greatest stress that a material can bear, after which it fractures and breaks.

10. Hysteresis Loss: Energy loss occurring during the deformation of a material, such as rubber. This is characterized by an increase in the internal energy of the molecules resulting in a rise in the temperature of the material. It is represented by the loop formed between the loading and unloading curves in a force-extension graph.

11. Brittle: A material, such as glass, that does not show plastic behavior, and suddenly snaps on reaching its elastic limit.

12. Ductility: The property of a material referring to its ability to undergo plastic deformation and have some permanent extension. This property enables materials, such as copper, to be drawn out or hammered thin without breaking

13. Stiffness: A measure of the degree of resistance of a material to deformation stress. The more stiff the material, the greater is the amount of force required to produce the same amount of extension

Properties of Materials and Hooke’s Law

, where ‘k’ is the spring constant

Elastic potential energy (E.P.E.) is the area underneath the force-extension graph

For similar springs in series

n = number of springs,

Where, for a single spring,

extension = e

and

spring constant = k

For similar springs in parallel

, where ‘σ’ represents tensile stress

, where ‘ε’ represents the tensile strain

, where ‘E’ represents the Young Modulus

• WAVES:

1. Amplitude: The maximum displacement of a particle on a wave from its mean position.

2. Phase Difference: The phase difference between two particles along the wave is the fraction of a cycle by which one moves behind the other. It has the formula: phase difference between two points = (the distance between the two points ÷ the wavelength) × 2π. It is a scalar quantity measured in radians (rad).

3. Period: The time taken for the completion of one full oscillation. It is a scalar quantity measured in the SI unit second (s).

4. Frequency: The number of complete wave oscillations per second. It is given by the formula f=1/T and is a scalar quantity measured in the SI unit hertz (Hz).

5. Wavelength: The distance between two successive particles moving in phase. It is a scalar quantity measured in the SI unit meter (m).

6. Wave Speed: The distance travelled per second by a wave. It has the formula v = fλ and is a scalar quantity measured in the SI unit meter per second (ms-1).

7. Particles in Phase: Particles on a wave that acquire their individual maximum and minimum displacements at the same time.

8. Intensity: The energy delivered by a wave per unit area per unit time to the surface on which the wave is incident. It has the formula I = E/At and is a scalar quantity measured in the SI units watt per meter square (Wm-2) or joule per meter square per second (Jm-2s-1).

9. Transverse Wave: A wave in which the direction of vibrations are in a plane normal to the direction of propagation of energy.

10. Longitudinal Wave: A wave in which the direction of vibrations are parallel to the direction of propagation of energy.

11. Polarization: A process by which the oscillations on a wave are made to occur in one plane only. Polarization is a phenomenon associated only with transverse waves. Longitudinal waves cannot be polarized.

12. Stationary Wave: A stationary wave is the result of interference between two waves of equal frequency, wavelength and amplitude, travelling along the same line with the same speed but in

opposite directions. The wave energy remains localised and the wave form does not move in the direction of either the incident wave or the reflected wave.

13. Electromagnetic Wave: A type of transverse wave that is propagated by the simultaneous periodic variations of electric and magnetic field intensity and include radio waves, micro waves, infrared, visible light, ultraviolet, X-rays, and gamma rays. These waves do not require a medium to propagate.

• SUPERPOSITION:

1. Principle of Superposition: When two or more waves meet in a region or interact to form a new wave whose displacement is due to the net amplitude at every point of interaction.

2. Diffraction: The process where a wave spreads out into regions or spaces where it would not have previously been experienced if it had travelled in a straight line, due to its passage through a narrow gap on which the wave front was incident.

3. Interference: Interference occurs when two or more waves meet at a point such that there is an overall change in the intensity or displacement

4. Coherence: When waves maintain a constant phase relationship during propagation.

5. Harmonic: An overtone whose vibration frequency is an integral multiple of the fundamental frequency and at which resonance occurs.

6. Antinode: A point on a stationary wave at which maximum displacement occurs.

7. Node: A point on a stationary wave at which zero displacement occurs, i.e. the point is stationary.

Waves

, where ‘I’ represents intensity of the wave, ‘E’ represents incident energy, ‘A’ represents area,

and ‘t’ represents time.

, where ‘r’ represents radius

, where ‘a’ represents amplitude

Double Slit Experiment

, where ‘x’ represents the fringe width, ‘λ’ represents the wavelength, ‘D’ represents the

distance between the slits and the screen, and ‘a’ represents the distance between the two slits.

Diffraction Grating

, where ‘d’ represents the grating spacing and ‘N’ represents the number of slits per meter

, where ‘d’ represents the grating spacing, ‘ ’ represents the sin of the angle between order ‘n’ and the central fringe, ‘n’ represents the order number, and ‘λ’ represents the wavelength.

Pipe closed at one end

, where ‘ ’ represents frequency of the nth overtone, and ‘ ’ represents the fundamental frequency

Pipe open

NOTE:

The following are fixed quantities that you are required to know:

Speed of light:

Speed of sound:

Mass of a proton or neutron:

Charge on a proton:

Mass of an electron:

Charge on an electron:

Value of e: