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Formulae 1 Mechanical = = = β„Ž = βˆ† βˆ† = = β„Ž = βˆ† βˆ† = β„Ž β„Ž Equations of motion = + = 1 2 ( + ) = + 1 2 2 2 = 2 + 2 Projectile Vertical : Time for maximum height, t

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Page 1: Physics Formula

Formulae

1

Mechanical

π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ 𝑠𝑝𝑒𝑒𝑑 =π‘‘π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’

π‘‘π‘–π‘šπ‘’

𝑣 =π‘₯

𝑑

π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦ =π‘β„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 π‘‘π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘

π‘‘π‘–π‘šπ‘’ π‘‘π‘Žπ‘˜π‘’π‘›

𝑣 =βˆ†π‘ 

βˆ†π‘‘

𝑠𝑝𝑒𝑒𝑑 =𝑑

𝑑

π‘Žπ‘£π‘’π‘Ÿπ‘Žπ‘”π‘’ π‘Žπ‘π‘π‘’π‘™π‘’π‘Ÿπ‘Žπ‘‘π‘–π‘œπ‘› =π‘β„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦

π‘‘π‘–π‘šπ‘’ π‘‘π‘Žπ‘˜π‘’π‘›

π‘Ž =βˆ†π‘£

βˆ†π‘‘

π‘‘π‘–π‘ π‘π‘™π‘Žπ‘π‘’π‘šπ‘’π‘›π‘‘ = π‘Žπ‘Ÿπ‘’π‘Ž π‘’π‘›π‘‘π‘’π‘Ÿ π‘‘β„Žπ‘’ π‘”π‘Ÿπ‘Žπ‘β„Ž

Equations of motion

𝑣 = 𝑒 + π‘Žπ‘‘

𝑠 =1

2(𝑒 + 𝑣)𝑑

𝑠 = 𝑒𝑑 +1

2π‘Žπ‘‘2

𝑣2 = 𝑒2 + 2π‘Žπ‘ 

Projectile

Vertical :

Time for maximum height, t

Page 2: Physics Formula

Formulae

2

𝑑 =𝑒 sin πœƒ

𝑔

Instantaneous height, y

𝑦 = (𝑒 sin πœƒ) 𝑑 βˆ’1

2𝑔𝑑

Total time taken, T

𝑇 =2𝑒 sin πœƒ

𝑔

Horizontal :

Instantaneous displacement, x

π‘₯ = (𝑒 cos πœƒ) 𝑑

Range, R

𝑅 =𝑒2 sin 2πœƒ

𝑔

Newton’s Second Law of Motion

𝐹 = π‘šπ‘Ž

Weight

π‘Š = π‘šπ‘”

Moment=force x distance from pivot

π‘šπ‘œπ‘šπ‘’π‘›π‘‘ = 𝐹 Γ— π‘₯1

Moment of anti-clockwise=Moment of clockwise

Work done

π‘Š = 𝐹 Γ— 𝑠

π‘Š = 𝐹𝑠 cos πœƒ

Gravitational Potential Energy

Page 3: Physics Formula

Formulae

3

πΆβ„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 𝑔. 𝑝. 𝑒 = π‘€π‘’π‘–π‘”β„Žπ‘‘ Γ— π‘β„Žπ‘Žπ‘›π‘”π‘’ 𝑖𝑛 β„Žπ‘’π‘–π‘”β„Žπ‘‘

𝐸𝑝 = π‘šπ‘”β„Ž

Kinetic Energy

𝐾𝑖𝑛𝑒𝑑𝑖𝑐 πΈπ‘›π‘’π‘Ÿπ‘”π‘¦ =1

2Γ— π‘šπ‘Žπ‘ π‘  Γ— 𝑠𝑝𝑒𝑒𝑑2

πΈπ‘˜ =1

2π‘šπ‘£2

GPE –KE Transformation

π‘‘π‘’π‘π‘Ÿπ‘’π‘Žπ‘ π‘’ 𝑖𝑛 𝑔. 𝑝. 𝑒 = π‘”π‘Žπ‘–π‘› 𝑖𝑛 π‘˜. 𝑒

Efficiency

𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 𝑒𝑠𝑒𝑓𝑒𝑙 π‘œπ‘’π‘‘π‘π‘’π‘‘ π‘’π‘›π‘’π‘Ÿπ‘”π‘¦

π‘‘π‘œπ‘‘π‘Žπ‘™ 𝑖𝑛𝑝𝑒𝑑 π‘’π‘›π‘’π‘Ÿπ‘”π‘¦Γ— 100%

Power

π‘π‘œπ‘€π‘’π‘Ÿ =π‘€π‘œπ‘Ÿπ‘˜ π‘‘π‘œπ‘›π‘’

π‘‘π‘–π‘šπ‘’ π‘‘π‘Žπ‘˜π‘’π‘›

𝑃 =π‘Š

𝑑

π‘π‘œπ‘€π‘’π‘Ÿ = π‘“π‘œπ‘Ÿπ‘π‘’ Γ— π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦

𝑃 = 𝐹 Γ— 𝑣

Linear momentum

π‘šπ‘œπ‘šπ‘’π‘›π‘‘π‘’π‘š = π‘šπ‘Žπ‘ π‘  Γ— π‘£π‘’π‘™π‘œπ‘π‘–π‘‘π‘¦

𝑝 = π‘šπ‘£

In a closed system:

total momentum of object before collision=total momentum of object after collision

π‘šπ΄π‘’π΄ + π‘šπ΅π‘’π΅ = π‘šπ΄π‘£π΄ + π‘šπ΅π‘£π΅

Relative velocity

𝑣𝐡 βˆ’ 𝑣𝐴 = βˆ’(𝑒𝐡 βˆ’ 𝑒𝐴)

Change in momentum

Page 4: Physics Formula

Formulae

4

βˆ†π‘ = 𝑝𝑓 βˆ’ 𝑝𝑖

Impulse

βˆ†π‘ = 𝐹 Γ— βˆ†π‘‘

Density

𝑑𝑒𝑛𝑠𝑖𝑑𝑦 =π‘šπ‘Žπ‘ π‘ 

π‘£π‘œπ‘™π‘’π‘šπ‘’

𝜌 =π‘š

𝑉

Pressure

π‘π‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’ =π‘›π‘œπ‘Ÿπ‘šπ‘Žπ‘™ π‘“π‘œπ‘Ÿπ‘π‘’

π‘π‘Ÿπ‘œπ‘ π‘  βˆ’ π‘ π‘’π‘π‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘Ÿπ‘’π‘Ž

𝑝 =𝐹

𝐴

Pressure in a fluid

𝑝 = πœŒπ‘”β„Ž

Force constant

π‘˜ =𝐹

π‘₯

Strain

π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘› =𝑒π‘₯π‘‘π‘’π‘›π‘ π‘–π‘œπ‘›

π‘œπ‘Ÿπ‘–π‘”π‘–π‘›π‘Žπ‘™ π‘™π‘’π‘›π‘”π‘‘β„Ž

π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘› =π‘₯

𝐿

Stress

π‘ π‘‘π‘Ÿπ‘’π‘ π‘  =π‘“π‘œπ‘Ÿπ‘π‘’

π‘π‘Ÿπ‘œπ‘ π‘  βˆ’ π‘ π‘’π‘π‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘Ÿπ‘’π‘Ž

Page 5: Physics Formula

Formulae

5

π‘ π‘‘π‘Ÿπ‘’π‘ π‘  =𝐹

𝐴

Young modulus

π‘Œπ‘œπ‘’π‘›π‘” π‘šπ‘œπ‘‘π‘’π‘™π‘’π‘  = π‘ π‘‘π‘Ÿπ‘’π‘ π‘ 

π‘ π‘‘π‘Ÿπ‘Žπ‘–π‘›

𝐸 =𝜎

πœ€

Elastic potential energy

𝐸 =1

2𝐹π‘₯

𝐸 =1

2π‘˜π‘₯2

Electric field strength

𝐸 =𝐹

𝑄

𝐸 =𝑉

𝑑

Current

π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ =π‘β„Žπ‘Žπ‘Ÿπ‘”π‘’

π‘‘π‘–π‘šπ‘’

π‘β„Žπ‘Žπ‘Ÿπ‘”π‘’ = π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ Γ— π‘‘π‘–π‘šπ‘’

βˆ†π‘„ = πΌβˆ†π‘‘

Resistance

π‘Ÿπ‘’π‘ π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ =π‘π‘œπ‘‘π‘’π‘›π‘‘π‘–π‘Žπ‘™ π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’

π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘

𝑅 =𝑉

𝐼

𝑉 = 𝐼𝑅

Electrical Power

π‘π‘œπ‘€π‘’π‘Ÿ =π‘’π‘›π‘’π‘Ÿπ‘”π‘¦ π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘“π‘’π‘Ÿπ‘Ÿπ‘’π‘‘

π‘‘π‘–π‘šπ‘’ π‘‘π‘Žπ‘˜π‘’π‘›

𝑃 =βˆ†π‘Š

βˆ†π‘‘

Page 6: Physics Formula

Formulae

6

βˆ†π‘Š = π‘‰βˆ†π‘„

𝑃 = 𝑉𝐼

Power and Resistance

𝑃 = 𝐼2𝑅

𝑃 =𝑉2

𝑅

Calculating energy

π‘π‘œπ‘€π‘’π‘Ÿ = π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ Γ— π‘£π‘œπ‘™π‘‘π‘Žπ‘”π‘’

π‘’π‘›π‘’π‘Ÿπ‘”π‘¦ = π‘π‘œπ‘€π‘’π‘Ÿ Γ— π‘‘π‘–π‘šπ‘’

π‘’π‘›π‘’π‘Ÿπ‘”π‘¦ π‘‘π‘Ÿπ‘Žπ‘›π‘ π‘“π‘’π‘Ÿπ‘Ÿπ‘’π‘‘ = π‘π‘’π‘Ÿπ‘Ÿπ‘’π‘›π‘‘ Γ— π‘£π‘œπ‘™π‘‘π‘Žπ‘”π‘’ Γ— π‘‘π‘–π‘šπ‘’

βˆ†π‘Š = πΌπ‘‰βˆ†π‘‘

Kirchhoff’s 1st Law

𝛴Iin=𝛴Iout

Kirchhoff’s 2nd

Law

𝛴E=𝛴V

Resistors in series

𝑅 = 𝑅1 + 𝑅2 + 𝑅3 … ..

Resistors in parallel

1

𝑅=

1

𝑅1+

1

𝑅2+

1

𝑅3+ β‹―

V-I Graph

π‘Ÿπ‘’π‘ π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ =1

π‘”π‘Ÿπ‘Žπ‘‘π‘–π‘’π‘›π‘‘ π‘œπ‘“ π‘”π‘Ÿπ‘Žπ‘β„Ž

Resistivity

π‘Ÿπ‘’π‘ π‘–π‘ π‘‘π‘–π‘£π‘–π‘‘π‘¦ = π‘Ÿπ‘’π‘ π‘–π‘ π‘‘π‘Žπ‘›π‘π‘’ Γ—π‘π‘Ÿπ‘œπ‘ π‘  βˆ’ π‘ π‘’π‘π‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘Ÿπ‘’π‘Ž

π‘™π‘’π‘›π‘”π‘‘β„Ž

Page 7: Physics Formula

Formulae

7

𝜌 =𝑅𝐴

𝐿

Internal resistance

𝐸 = 𝐼(𝑅 + π‘Ÿ)

Potential dividers

π‘‰π‘œπ‘’π‘‘ = βŒŠπ‘…2

𝑅1 + 𝑅2βŒ‹ Γ— 𝑉𝑖𝑛

Frequency

𝑓 =1

𝑇

Period

𝑇 =1

𝑓

Intensity

𝑖𝑛𝑑𝑒𝑛𝑠𝑖𝑑𝑦 =π‘π‘œπ‘€π‘’π‘Ÿ

π‘π‘Ÿπ‘œπ‘ π‘  βˆ’ π‘ π‘’π‘π‘‘π‘–π‘œπ‘›π‘Žπ‘™ π‘Žπ‘Ÿπ‘’π‘Ž

Intensity and amplitude

𝑖𝑛𝑑𝑒𝑛𝑠𝑖𝑑𝑦

π‘Žπ‘šπ‘π‘™π‘–π‘‘π‘’π‘‘π‘’2= π‘π‘œπ‘›π‘ π‘‘π‘Žπ‘›π‘‘

Wave speed

𝑣 = 𝑓 Γ— πœ†

Speed of light

𝑐 = π‘“πœ†

Destructive interference

π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ =1

2πœ†, 1

1

2πœ†, 2

1

2πœ†, … ..

π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ = (𝑛 +1

2)πœ†

Constructive interference

π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ = 0, πœ†, 2πœ†, 3πœ† ….

Page 8: Physics Formula

Formulae

8

π‘π‘Žπ‘‘β„Ž π‘‘π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ = π‘›πœ†

Young Double-slit

πœ† =π‘Žπ‘₯

𝐷

a=slit separation

x=fringe separation

D=slit-to-screen distance

Determining πœ† with a grating

𝑑 sin πœƒ = π‘›πœ†

Air column (Open ends)

Page 9: Physics Formula

Formulae

9

𝐿 =π‘›πœ†

2

𝑓 =𝑛𝑣

2𝐿

Air column (Close ends)

Page 10: Physics Formula

Formulae

10

Error

πœ† = 2(𝑙2 βˆ’ 𝑙1)

Sting

Page 11: Physics Formula

Formulae

11

Air Closed

Air open

Page 12: Physics Formula

Formulae

12

Radioactivity

Ξ±-decay

𝐴𝑍

𝑋 →𝐴 βˆ’ 4𝑍 βˆ’ 2

π‘Œ +42

∝

Ξ²-decay

10

𝑛 β†’11

𝑝 +0

βˆ’1𝑒 + π‘’π‘›π‘’π‘Ÿπ‘”π‘¦

Ξ³-emission


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