Microsoft Word - List of Equation F4.doc

Physics Equation List :Form 4Introduction to Physics

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17http://www.one-school.net/notes.html

Relative Deviation

Relative Deviation =

Mean Deviation 100% Mean Value

Prefixes

PrefixesValueStandard formSymbol

Tera1 000 000 000 0001012T

Giga1 000 000 000109G

Mega1 000 000106M

Kilo1 000103k

deci0.110-1d

centi0.0110-2c

milli0.00110-3m

micro0.000 00110-6

nano0.000 000 00110-9n

pico0.000 000 000 00110-12p

Units for Area and Volume

1 m = 102 cm(100 cm)

-21

1 m2 = 104 cm2(10,000 cm2)1 m3 = 106 cm3(1,000,000 cm3)

1 cm= 10

m(m )100

1 cm2 = 10-4 m2(

1 cm3 = 10-6 m3(

1

10,0001

m2 )

m3 )

1,000,000

Average Speed

Force and Motion

Average Speed Total DistanceTotal Time

Velocityv st

v = velocity(ms-1) s = displacement(m)t = time(s)

Acceleration

a v ut

a = acceleration(ms-2)v = final velocity(ms-1)u = initial velocity(ms-1)t =time for the velocity change(s)

Equation of Linear Motion

Linear MotionMotion withconstant velocityMotion withconstant accelerationMotion withchanging acceleration

v stv u ats 1 (u v)t2s ut 1 at 22v2 u2 2as

Using Calculus (In Additional Mathematics Syllabus)

u = initial velocity(ms-1)v = final velocity(ms-1)a = acceleration(ms-2)s = displacement(m)t = time(s)

Ticker Tape

Finding Velocity:

velocity

snumber of ticks

0.02s

1 tick = 0.02s

Finding Acceleration:

a v ut

Graph of Motion

a = acceleration(ms-2)v = final velocity(ms-1)u = initial velocity(ms-1)t = time for the velocity change(s)

Gradient of a GraphThe gradient 'm' of a line segment between two points and is defined as follows:

Gradient, m Change in y coordinate, yChange in x coordinate, xorm yx

Displacement-Time GraphVelocity-Time Graph

Gradient = Velocity (ms-1)Gradient = Acceleration (ms-2)Areainbetweenthegraphandx-axis= Displacement

Momentum

p m v

p = momentum(kg ms-1) m = mass(kg)v = velocity(ms-1)

Principle of Conservation of Momentum

m1u1 m2u2

m1v1 m2v2

m1 = mass of object 1(kg)m2 = mass of object 2(kg)u1 = initial velocity of object 1(ms-1)u2 = initial velocity of object 2(ms-1)v1 = final velocity of object 1(ms-1)v2 = final velocity of object 2(ms-1)

Newtons Law of Motion Newtons First Law

In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).

Newtons Second Law

Fmv mut

The rate of change of momentum of a body is directly proportional to the resultant force acting on the body and is in the same direction.

F = Net Force(N or kgms-2) m = mass(kg)

F ma

a = acceleration(ms-2)

ImplicationWhen there is resultant force acting on an object, the object will accelerate(moving faster, moving slower or change direction).

Newtons Third Law

Newton's third law of motion states that for every force, there is a reaction force with the same magnitude but in the opposite direction.

Impulse

Impulse FtImpulse mv mu

F = force(N)t = time(s)

m = mass(kg)v = final velocity(ms-1)u = initial velocity(ms-1)

Impulsive Force

F mv mut

F = Force(N or kgms-2)t = time(s)m = mass(kg)v = final velocity(ms-1)u = initial velocity(ms-1)

Gravitational Field Strength

g Fm

g = gravitational field strength(N kg-1)F = gravitational force(N or kgms-2)m = mass(kg)

Weight

W mgW = Weightm = mass(N or kgms-2)(kg)g = gravitational field strength/gravitational acceleration(ms-2)

Vertical Motion

If an object is release from a high position: The initial velocity, u = 0. The acceleration of the object = gravitational acceleration = 10ms-2(or 9.81 ms-2). The displacement of the object when it reach the ground = the height of the original position, h. If an object is launched vertically upward: The velocity at the maximum height, v = 0. The deceleration of the object = -gravitational acceleration = -10ms-2(or -9.81 ms-2). The displacement of the object when it reach the ground = the height of the original position, h.

Lift

In Stationary

R mg When a man standing inside an elevator, there are two forces acting on him.(a) His weight which acting downward.(b) Normal reaction (R), acting in the opposite direction of weight.

The reading of the balance is equal to the normal reaction.

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Moving Upward with positive accelerationMoving downward with positive acceleration

R mg maR mg ma

Moving Upward with constant velocityMoving downward with constant velocity.

R mgR mg

Moving Upward with negative accelerationMoving downward with negative acceleration

R mg maR mg ma

Smooth Pulley

With 1 Load

T1 = T2Moving with uniform speed:

T1 = mg

Stationary:

T1 = mgAccelerating:

T1 mg = ma

With 2 Loads

Finding Acceleration:(If m2 > m1)m2g m1g = (m1+ m2)a

Finding Tension:(If m2 > m1)T1 = T2T1 m1g = ma m2g T2 = ma

Vector

Vector Addition (Perpendicular Vector)x2 y2

Magnitude =

Direction = tan1 | y || x |

Vector Resolution

| x || p | sin

| y || p | cos

Forces In Equilibrium

Component parallel to the plane= mgsin

Component perpendicular to the plane= mgcosONE-SCHOOL.NETInclined Plane

T3 mg

T3 mg

T2 sinmg

T2 cos

T1 cos

T2 cosT1T1 tanmg

T2 sinT1 sinmg

Work Done

W Fx cos

W = Work Done(J or Nm)F = Force(N or kgms-2)x = displacement(m)= angle between the force and the direction of motion(o)

When the force and motion are in the same direction.

W Fs

W = Work Done(J or Nm)F = Force(N or kgms-2)s = displacement(m)

Energy

Kinetic EnergyONE-SCHOOL.NET

E1 mv2K2

EK = Kinetic Energy(J)m = mass(kg)v = velocity(ms-1)

Gravitational Potential Energy

EP mgh

EP = Potential Energy(J)m = mass(kg)g = gravitational acceleration(ms-2) h = height(m)

Elastic Potential Energy

E1 kx2P2E1 FxP2

EP = Potential Energy(J)k = spring constant(N m-1)x = extension of spring(m)

F = Force(N)

Power and Efficiency

Power

P Wt

P = power(W or Js-1)W = work done(J or Nm)E = energy change(J or Nm)

P Et

t = time(s)

Efficiency

Efficiency =

Useful Energy 100% Energy

Efficiency =

Or

Power Output 100% Power Input

Hookes Law

F kx

F = Force(N or kgms-2)k = spring constant(N m-1) x = extension or compression of spring(m)

Force and Pressure

Density

mV

Pressure

= density(kg m-3)m = mass(kg)V = volume(m3)

P F

P = Pressure(Pa or N m-2)A = Area of the surface(m2)

AF = Force acting normally to the surface(N or kgms-2)

Liquid PressureP hg

h = depth(m)= density(kg m-3)g = gravitational Field Strength(N kg-1)

Pressure in Liquid

P Patm hg

h = depth(m)= density(kg m-3)g = gravitational Field Strength(N kg-1)Patm = atmospheric Pressure(Pa or N m-2)

Gas Pressure

Manometer

P Patm

hg

Pgas = Pressure(Pa or N m-2) Patm = Atmospheric Pressure(Pa or N m-2) g = gravitational field strength (N kg-1)

U=tube

Pressure in a Capillary Tube

h11

h2 2

Barometer

Pgas = gas pressure in the capillary tube(Pa or N m-2) Patm = atmospheric pressure(Pa or N m-2)h = length of the captured mercury(m)= density of mercury(kg m-3)g = gravitational field strength(N kg-1)

Pressure in unit cmHgPressure in unit Pa

Pa = 0Pa = 0

Pb = 26Pb = 0.261360010

Pc = 76Pc = 0.761360010

Pd = 76Pd = 0.761360010

Pe = 76Pe = 0.761360010

Pf = 84Pf = 0.841360010

(Density of mercury = 13600kgm-3)

Pascals Principle

F1 F2A1A2F1 = Force exerted on the small pistonA1 = area of the small pistonF2 = Force exerted on the big piston A2 = area of the big piston

Archimedes Principle

Weight of the object, W 1V1 gUpthrust, F 2V2 g1 = density of wooden blockV1 = volume of the wooden block2 = density of waterV2 = volume of the displaced water g = gravitational field strength

Density of water > Density of wood

F = T + WVg T mgDensity of Iron > Density of water

T + F = WVg T mg

ONE-SCHOOL.NETHeat

Heat Change

Q mc

m = mass(kg)c = specific heat capacity(J kg-1 oC-1)= temperature change(o)

Electric HeaterMixing 2 Liquid

Energy Supply, E PtEnergy Receive, Q mc

Energy Supply, E = Energy Receive, QPt mcE = electrical Energy (J or Nm)P = Power of the electric heater (W) t = time (in second)(s)

Q = Heat Change (J or Nm) m = mass(kg)c = specific heat capacity (J kg-1 oC-1)= temperature change(o)Heat Gain by Liquid 1 = Heat Loss by Liquid 2m1c11 m2c22m1 = mass of liquid 1c1 = specific heat capacity of liquid 11 = temperature change of liquid 1

m2 = mass of liquid 2c2 = specific heat capacity of liquid 22 = temperature change of liquid 2

Specific Latent Heat

Q mL

Q = Heat Change(J or Nm)m = mass(kg)L = specific latent heat(J kg-1)

Boyles Law

P1V1 P2V2

(Requirement: Temperature in constant)Pressure Law

(Requirement: Volume is constant)

P1 P2 T1T2

V1 V2 T1T2

ONE-SCHOOL.NETCharless Law

(Requirement: Pressure is constant)Universal Gas Law

P1V1 T1

P2V2T2

Refractive Index

P = Pressure(Pa or cmHg .)V = Volume(m3 or cm3)T = Temperature(MUST be in K(Kelvin))

Light

Snells LawReal depth/Apparent Depthn sin isin rn = refractive index(No unit)i = angle of incident(o) r = angle of reflection(o)

n Ddn = refractive index(No unit)D = real depth(m or cm) d = apparent depth(m or cm)

Speed of lightn cvn = refractive index(No unit)c = speed of light in vacuum(ms-1)v = speed of light in a medium (like water, glass )(ms-1)Total Internal Reflectionn 1sin cn = refractive index(No unit) c = critical angle(o)

ONE-SCHOOL.NETLens

Power

P 1f

P = Power(D(Diopter))f = focal length(m)

Linear Magnification

m hiho

m vu

hi vhou

m = linear magnification(No unit)

u = distance of object(m or cm)

v = distance of image(m or cm)

hi = heigth of image ho = heigth of object(m or cm) (m or cm)

Lens Equation

1 1 1

Conventional symbola

uvf

ONE-SCHOOL.NETAstronomical Telescope

Magnification,

m PePo

m fofe

m = linear magnification Pe = Power of the eyepiecePo = Power of the objective lens fe = focal length of the eyepiecefo = focal length of the objective lens

Distance between eye lens and objective lens

d = fo + fe

d = Distance between eye lens and objective lens fe = focal length of the eyepiecefo = focal length of the objective lens

Compound Microscope

Magnification

m m1 m2Height of first image , I1 Height of second image, I2Height of objectHeight of first image , I1Height of second image, I2Height of object, I1

m = Magnification of the microscopem1 = Linear magnification of the object lens m2 = Linear magnification of the eyepiece

Distance in between the two lens

d > fo + fe

d = Distance between eye lens and objective lens fe = focal length of the eyepiecefo = focal length of the objective lens

Physics Equation List :Form 5Wave Oscillation

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18

f1T

f = frequency(Hz or s-1)T = Period(s)

Displacement-Time Graph

Amplitude, Period and Frequency can be found from a Displacement-Time Graph

Wave

v f

v = velocity(ms-1)

f = frequency(Hz or s-1)= wavelength(m)

Displacement-Distance Graph

= Wavelength

Interference

19

= Wavelength

axD

a = Distance between the two wave sourcesx = Distance between two successive anti-node lines or node lines D = Distance from the wave sources to the plane where x is measured.

Summary

Electricity Sum of charge

Q ne

Q = Chargen = number of charge particles e = charge of 1 particle

Current

I Qt

Q = Charge I = Current t = time

Potential Difference

20V = WV = potential difference, (V or JC-1)

W = energy(J)QQ = charge(C)

Ohms Law and Resistance

V IR

V = potential difference,(V or JC-1)

I = Current(A or Cs-1)R = Resistance()

Resistance

R R1 R2R ( 1 1 1 )1R1R2R3

CurrentSeries CircuitParallel Circuit

The current flow into a resistor = the current flow inside the resistor = the current flows out from the resistorIA = IB = IC

In a series circuit, the current at any points of the circuit is the same.The current flow into a parallel circuit is equal to the sum of the current in each branches of the circuit.

I = I1 + I2Example

If the resistance of the 2 resistors is the same, current will be divided equally to both of the resistor.

Potential and Potential DifferenceSeries CircuitParallel Circuit

The sum of the potential difference across individual resistor in between 2 points in a series circuit is equal to the potential difference across the two point.

V = V1 + V2

Example

The potential difference across all the resistor in a parallel circuit is the same.

V = V1 = V2

Example

Potential Difference and Electromotive Force

If we assume that there is no internal resistance in the cell, the potential difference across the cell is equal to the e.m.f. of the cell.

21Electromotive Force and Internal Resistance

22E I (R r)

orE V Ir

E = Electromotive Force(V)r = internal resistance()V = potential difference,(V or JC-1)I = Current(A or Cs-1)R = Resistance()2 methods to find the internal resistance and electromotive forcea. Open Circuit Close Circuit methodOpen CircuitClose Circuit

In open circuit ( when the switch is off), the voltmeter shows the reading of the e.m.f.In close circuit ( when the switch is on), the voltmeter shows the reading of the potential difference across the cell.

With the presence of internal resistance, the potential difference across the cell is always less than the e.m.f..

b. Linear Graph method

Electrical Energy

From the equation,

E = V + IrThereforeV = -rI + E

Gradient od the grapf, m= -internal resistance

Y intercept of the graph, c= electromotive force

E QV

E = Electrical Energy(J)Q = charge(C)V = potential difference(V or JC-1)

Electrical Power

P Wt

P IV

P I 2 RP V R2

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23

P = Power(W or Js-1)W = Work done/Energy change(J)t = Time(s)I = Current(A)V = Potential difference(V)R = Resistance()

Efficiency

Electrical efficiency =

output power 100% input power

Electromagnetism

Root mean Square Value

Vrms

Vp

Vrms = root mean square voltage(V) Vp = peak voltage(V)2

I pIrms 2

Irms = root mean square current(A) Ip = peak current(A)

Transformer

Input And Output Of A Transformer

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24VsNs

Vp = input (primary) potential difference(V) Vs = output (secondary) potential difference(V) Np = number of turns in primary coil

VpN p

Ns = number of turns in secondary coil

Power In A Transformer

Ideal Transformer

Vp = input (primary) potential difference(V) Vs = output (secondary) potential difference(V)

Vp I p

Vs I s

Ip = input (primary) current(A)

Is = output (secondary) current(A)Non-ideal transformer

Efficiency

Vs I sVp I p

100%

Power Transmission

2Steps to find the energy/power loss in the cablea. Find the current in the cable by the equation P=IVb. Find the Power lost in the cable by the equation P=I2R.ElectronicEnergy change of electron in an electron gun

Kinetic energy gain

electrical potential=energy

1 mv222eVm

v

eV

v = speed of electron(ms-1)V = potential difference across the electron gun(V) e = charge of 1 electron(C)m = mass of 1 electron(kg)

Cathode Ray Oscilloscope

Vertical scale = Y-gain control Horizontal scale = Time basePeriod = Time for 1 complete OscillationONE-SCHOOL.NET

25

Transistor - Potential Divider

Frequency,

f 1T

Potential difference across resistor R1=R1R1 R2VPotential difference across resistor R2=R2R1 R2V

Radioactivity

Alpha decay

A XA44

26Beta decay

Z

Z 2Y 2 He

AX

Z

A0Ye

Z 11

Gamma emission

1101n1 e0p

A XA

ZZ X

A = nucleon number Z = proton number

Half-life

N

(1)n N20

N = Amount of radioisotope particles after nth half life. N0 = Initial amount of radioisotope particles.n = number of half life

Nuclear Energy - Einstein Formula

E mc2

m = mass change(kg)c = speed of light(m s-1 )E = energy changed(J)