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SPM-Physics-Formula-List-Form4 + 5
Microsoft Word - List of Equation F4.doc
Physics Equation List :Form 4Introduction to Physics
ONE-SCHOOL.NET
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.
ONE-SCHOOL.NET
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
ONE-SCHOOL.NET
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
ONE-SCHOOL.NET
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
ONE-SCHOOL.NET
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)