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Uploaded by Teh Lee Cheng

Physics Formulas: Cheat Sheet for High School/College

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Chapter #1- Uncertainty
π‘₯ =𝐴+𝐡
π‘₯ =𝐴−𝐡
π‘₯ =𝐴×𝐡
π‘₯=
}
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π‘₯=𝐴
π‘₯ = π‘π‘œπ‘›π‘ π‘‘. 𝐴
𝛿π‘₯ = 𝛿𝐴 + 𝛿𝐡
𝛿π‘₯ 𝛿𝐴 𝛿𝐡
=
+
π‘₯
𝐴
𝐡
}
𝛿π‘₯
𝛿𝐴
= 𝐡.
π‘₯
𝐴
βˆ†π‘₯ = π‘₯ − π‘₯
Vectors:
𝑑=
𝑑 +𝑑
π‘π‘œπ‘  πœƒ =
𝑑
𝑑
𝑑 = 𝑑 π‘π‘œπ‘  πœƒ
𝑠𝑖𝑛 πœƒ =
d
𝑑
𝑑
𝑑 = 𝑑 𝑠𝑖𝑛 πœƒ
dy
θ
π‘œπ‘π‘
𝑠𝑖𝑛 πœƒ =
β„Žπ‘¦π‘
dx
π‘Žπ‘‘π‘—
π‘π‘œπ‘  πœƒ =
β„Žπ‘¦π‘
π‘‘π‘Žπ‘› πœƒ =
π‘œπ‘π‘
π‘Žπ‘‘π‘—
Chapter #2- Kinematics
βˆ†
π‘Ž=βˆ†
a=acceleration; v= velocity; t=time
π‘Ž=
v= final velocity; u= initial velocity
𝑣 = 𝑒 + π‘Žπ‘‘
𝑠 = 𝑣𝑑
𝑣
=
s= displacement
𝑒+𝑣
2
𝑠 = 𝑒𝑑 + 1 2 π‘Žπ‘‘
For flight time from rest:
𝑑 =
g=acceleration of free fall; h=height of fall; t=time
𝐾𝐸 = 𝐾𝐸 + π‘”π‘Žπ‘–π‘› 𝑖𝑛 𝐾𝐸
πΊπ‘Žπ‘–π‘› 𝑖𝑛 𝐾𝐸 = 𝐾𝐸 − 𝐾𝐸
𝐾𝐸 = 1 2 π‘šπ‘£
βˆ†πΎπΈ = 1 2 π‘š(𝑣 − 𝑣 )
βˆ†π‘ƒπΈ = βˆ†πΎπΈ with no external force, friction
𝑃𝐸 = π‘šπ‘”β„Ž
βˆ†π‘ƒπΈ = π‘šπ‘”(β„Ž − β„Ž )
Momentum:
𝑃 = π‘šπ‘£
P=momentum; m=mass-kg; v=velocity
βˆ†π‘ƒ = π‘š. βˆ†π‘£
βˆ†π‘ƒ
βˆ†π‘£
= π‘š.
βˆ†π‘‘
βˆ†π‘‘
βˆ†π‘ƒ
= π‘š. π‘Ž
βˆ†π‘‘
𝐹 = π‘šπ‘Ž
βˆ†
𝐹=βˆ†
2nd law of motion
βˆ†π‘ƒ = 𝐹 × βˆ†π‘‘
βˆ†P= impulse of force
𝑃 = π‘šπ‘£
𝑃 = (π‘šπ‘£)
𝑃 = π‘š .𝑣
𝑃 = π‘š. π‘š. 𝑣
𝑃
= π‘šπ‘£
π‘š
𝑃
1
= π‘šπ‘£
2π‘š 2
𝑃
= 𝐾𝐸
2π‘š
𝑃 = √2π‘šπΎπΈ
Law of conservation of momentum
𝐹 = −𝐹
βˆ†π‘ƒ
βˆ†π‘ƒ
=−
βˆ†π‘‘
βˆ†π‘‘
(𝑃 − 𝑃 ) = −(𝑃 − 𝑃 )
π‘š 𝑒 − π‘š 𝑒 = −π‘š 𝑣 + π‘š 𝑣
π‘€π‘œπ‘šπ‘’π‘›π‘‘π‘’π‘š π‘œπ‘“ π‘ π‘¦π‘ π‘‘π‘’π‘š π‘π‘’π‘“π‘œπ‘Ÿπ‘’ π‘π‘œπ‘™π‘™π‘–π‘ π‘–π‘œπ‘› = π‘€π‘œπ‘šπ‘’π‘›π‘‘π‘’π‘š π‘œπ‘“ π‘ π‘¦π‘ π‘‘π‘’π‘š π‘Žπ‘“π‘‘π‘’π‘Ÿ π‘π‘œπ‘™π‘™π‘–π‘ π‘–π‘œπ‘›
π‘š 𝑒 − π‘š 𝑒 = (π‘š + π‘š )𝑉 for if the bodies stick together after collision
for a perfectly elastic collision
𝑒 +𝑒 =𝑣 +𝑣
𝐹 = πœŒπ΄π‘£
F=force of flow of fluid; p=density; A=cross-sectional area; v=velocity
𝐹 = πœŒπ΄π‘£
FR = flow rate (kg s-1 );
π‘š = πœŒπ΄π‘£π‘‘
m=mass of fluid; t= time taken for ’m’ to flow
Chapter#3- Work, energy and Power
W=work; f=force; d=distance in direction of force
π‘Š = 𝑓×𝑑
π‘Š = 𝑓𝑑 π‘π‘œπ‘  πœƒ for an inclined plane
P=pressure; V=volume
π‘Š = 𝑃(𝑉 − 𝑉 )
π‘Š = 𝑓𝑑
π‘Š = 𝑃𝐴𝑑
π‘Š = 𝑃 × π΄π‘₯
π‘Š = 𝑃 × βˆ†π‘‰
π‘Š = 𝑃(𝑉 − 𝑉 )
Wf=work against friction
𝐺𝑃𝐸 − 𝐾𝐸 = π‘Š
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑃=
π‘œπ‘’π‘‘π‘π‘’π‘‘ π‘π‘œπ‘€π‘’π‘Ÿ
× 100%
𝑖𝑛𝑝𝑒𝑑 π‘π‘œπ‘€π‘’π‘Ÿ
P=Power; W=work; t=time
F=force; v=velocity
𝑃 = 𝐹𝑣
Chapter #4-Forces, density and pressure
𝑃=
P=pressure; f=force; a= surface area
𝑃 = πœŒπ‘”β„Ž for liquids
Po=atmospheric pressure
𝑃 = 𝑃 + πœŒπ‘”β„Ž
𝐹 = πœŒπ‘‰π‘”
F=upthrust; V=volume of liquid displaced; p=density of liquid
𝑇 =𝐹×𝑙
T=moment of force; F=force; l=length from pivot
𝑇 = 𝐹 × π‘™ π‘π‘œπ‘  πœƒ
𝑇=𝐹×
F
R
F
𝑙
2
F
θ
F
𝑇 = 𝐹 × 2𝑅
l
𝜌=
π‘š
𝑣
P=density; m=mass; v=volume
F
Chapter#5- Deformation of solids
F=force/load; k=spring constant; x=extension
π‘˜=
𝐹 = π‘˜π‘₯
π‘†π‘‘π‘Ÿπ‘Žπ‘–π‘› π‘’π‘›π‘’π‘Ÿπ‘”π‘¦ = 1 2 𝐹π‘₯
π‘†π‘‘π‘Ÿπ‘Žπ‘–π‘› π‘’π‘›π‘’π‘Ÿπ‘”π‘¦ = 1 2 π‘˜π‘₯
𝜎=
σ=stress; F=force/load; A=cross-sectional area
πœ€=
ε=strain; e=extension; l=length of spring
𝐸=
E=Young’s modulus
𝐸=
𝐹𝑙
𝑒𝐴
Chapter#6-Electricity
I=current; Q=Charge; t=time
𝐼=
𝑄 = 𝐼𝑑
π‘π‘œ. π‘œπ‘“ 𝑒 𝑠 π‘π‘’π‘Ÿ 𝑠𝑒𝑐 =
𝑄 = 𝑛𝑒
=𝑛
Q=Amount of charge on object; n=integer; e=elementary charge
N=Total no. of 𝑒 𝑠 π‘π‘’π‘Ÿ 𝑠𝑒𝑐; no. of 𝑒 𝑠 π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑 π‘£π‘œπ‘™π‘’π‘šπ‘’; 𝑉 = π‘£π‘œπ‘™π‘’π‘šπ‘’
I=current; A=cross-sectional area of wire; q=elementary charge; n=no. of
𝑒 𝑠 π‘π‘’π‘Ÿ 𝑒𝑛𝑖𝑑 π‘£π‘œπ‘™π‘’π‘šπ‘’; V=volume
𝐼 = π‘›π΄π‘žπ‘‰
R=resistance; ρ=resistivity; l=length; A=cross sectional area
𝑅=
𝜌=
π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘
π‘’π‘™π‘’π‘šπ‘’π‘›π‘‘π‘Žπ‘Ÿπ‘¦ π‘β„Žπ‘Žπ‘Ÿπ‘”π‘’
𝑅𝐴
𝑙
W=energy consumed; V=voltage; Q=transferred charge
𝑉=
π‘Š = 𝑉𝑄
𝑉 = 𝐼𝑅
𝐼=
𝑉
𝑅
𝑅=
𝑉
𝐼
𝑉 =𝑉 +𝑉
V=voltage; I=current; R=resistance
energy conservation principle; Kirchoff’s 2nd law
𝐼 𝑅 =𝐼 𝑅 +𝐼 𝑅
𝑅 =𝑅 +𝑅
for series only
𝑉
𝑅
=
𝑉
𝑅
𝐼=
𝑉
𝑅 +𝑅
𝑉 =
𝑉
×𝑅
𝑅 +𝑅
𝑉 =
𝑉
×𝑅
𝑅 +𝑅
𝐼 =𝐼 +𝐼
=
+
𝑅 =
𝑅 𝑅
𝑅 +𝑅
Principle of Kirchoff’s charge; 1st law of conservation
for parallel only
𝐼 =
𝐼
×𝑅
𝑅 +𝑅
𝐼 =
𝐼
×𝑅
𝑅 +𝑅
𝑃 = 𝑉𝐼
𝑃=𝐼 𝑅
𝑃=
P=power; V=voltage; I=current; R=resistance
𝑉
𝑅
𝑉 = 𝐸 − 𝐼𝑅
𝑉 = 𝐸 + 𝐼𝑅
battery being used up
battery being charged
null method
=
Chapter #7- Waves and superposition
𝑣 = 𝑓λ
v=speed of wave; f=frequency of wave; λ=wavelength
𝑓=
T=time period for one oscillation
𝐼=
I=intensity of wave; P=power; A=cross sectional area
𝐼∝𝐴
A=Amplitude
𝐼
𝐼
=
𝐴
𝐴
Doppler effect:
𝑓 =𝑓
𝑣
𝑣+𝑣
π‘“π‘œπ‘Ÿ π‘€β„Žπ‘’π‘› π‘ π‘œπ‘’π‘Ÿπ‘π‘’ 𝑖𝑠 π‘šπ‘œπ‘£π‘–π‘›π‘” π‘Žπ‘€π‘Žπ‘¦ π‘“π‘Ÿπ‘œπ‘š π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘’π‘Ÿ
𝑓 =𝑓
𝑣
𝑣−𝑣
π‘“π‘œπ‘Ÿ π‘€β„Žπ‘’π‘› π‘ π‘œπ‘’π‘Ÿπ‘π‘’ 𝑖𝑠 π‘šπ‘œπ‘£π‘–π‘›π‘” π‘‘π‘œπ‘€π‘Žπ‘Ÿπ‘‘π‘  π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘’π‘Ÿ
𝑓 = π‘œπ‘π‘ π‘’π‘Ÿπ‘£π‘’π‘‘ π‘“π‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦
𝑓 = π‘ π‘œπ‘’π‘Ÿπ‘π‘’ π‘“π‘Ÿπ‘’π‘žπ‘’π‘’π‘›π‘π‘¦
v=speed of sound
𝑣 = 𝑠𝑝𝑒𝑒𝑑 π‘œπ‘“ π‘ π‘œπ‘’π‘Ÿπ‘π‘’
π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ = 𝑛λ
for constructive interference
π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ = (𝑛 + 1 2)λ
for destructive interference
a=slit separation; λ=wavelength; x=fringe separation; D=distance between slits
and screen
πœ†=
d=distance between consecutive slits; θ=angle of nth order from central
maxima; n=order of maxima
𝑑 sin πœƒ = 𝑛λ
d=distance between consecutive slits; N=Number of slits per metre
𝑑=
πœ† = 2(𝑙 − 𝑙 )
𝑙 =length of tube for second harmonic
𝑙 =length of tube for first harmonic
𝑣 = 2𝑓(𝑙 − 𝑙 )
v=speed of wave; f=frequency
Chapter #8-Radioactivity
𝑋→
π‘Œ + 𝐻𝑒
alpha decay
𝑋→
π‘Œ+
beta decay
𝑒
gamma decay
𝑋 → 𝑋+𝛾
𝑛→ 𝑝+
𝑒+αΏ‘
𝛽 − π‘‘π‘’π‘π‘Žπ‘¦
𝑝→ 𝑛+
𝑒+𝑣
𝛽 + π‘‘π‘’π‘π‘Žπ‘¦
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