Please Do Not Write on This Sheet
Physics Formula Sheet Chapter 1: Introduction: The Nature of Science and Physics π₯=
βπ Β±
βπ 2
π
π¦ = π΄π¦ + π΅π¦ π
= βπ
π₯2 + π
π¦2
β 4ππ
2π π
ππππ’π ππ πΈπππ‘β = 6.38 Γ 106 π πππ π ππ πΈπππ‘β = 5.98 Γ 1024 ππ π = 3.00 Γ 108 π/π ππ2 πΊ = 6.673 Γ 10β11 ππ2 ππ΄ = 6.02 Γ 1023 π = 1.38 Γ 10β23 π½/πΎ π½ π
= 8.31 βπππ β
πΎ π = 5.67 Γ 10β8 π/(π2 β
πΎ) π = 8.99 Γ 109 π β
π2 /πΆ 2 ππ = β1.60 Γ 10β19 πΆ π0 = 8.85 Γ 10β12 πΆ 2 /(π β
π2 ) π0 = 4Ο Γ 10β7 π β
π/π΄ β = 6.63 Γ 10β34 π½ β
π ππ = 9.11 Γ 10β31 ππ ππ = 1.6726 Γ 10β27 ππ ππ = 1.6749 Γ 10β27 ππ πππ’ = 1.6605 Γ 10β27 ππ ππ π·πππ ππ‘π¦ ππ π€ππ‘ππ = 1000 3 π
Chapter 2: Kinematics π₯π₯ = π₯π β π₯0 π₯π‘ = π‘π β π‘0 π₯π₯ π₯π β π₯0 π£= = π₯π‘ π‘π β π‘0 π₯π£ π£π β π£0 π= = π₯π‘ π‘π β π‘0 π₯ = π₯0 + π£π‘ π£0 + π£ π£= 2 π£ = π£0 + ππ‘ 1 π₯ = π₯0 + π£0 π‘ + ππ‘ 2 2 π£ 2 = π£02 + 2π(π₯ β π₯0 ) π π = 9.80 2 π
Chapter 3: Two-Dimensional Kinematics π΄π₯ = π΄ πππ π π΄π¦ = π΄ π ππ π π
π₯ = π΄π₯ + π΅π₯
π = π‘ππβ1
π
π¦ π
π₯
2 π£0π¦ 2π 2 π£0 π ππ 2π0 π
= π π£π₯ = π£ πππ π π£π¦ = π£ π ππ π
β=
π£ = βπ£π₯2 + π£π¦2 π = π‘ππβ1
π£π¦ π£π₯
Chapter 4: Dynamics: Forces and Newtonβs Laws of Motion πΉπππ‘ = ππ π€ = ππ
Chapter 5: Further Applications of Newtonβs Laws: Friction, Drag, and Elasticity ππ β€ ππ π ππ = ππ π 1 πΉπ· = πΆππ΄π£ 2 2 πΉπ = 6ππππ£ πΉ = ππ₯π₯ 1πΉ π₯πΏ = πΏ ππ΄ 0 πΉ π π‘πππ π = π΄ π₯πΏ π π‘ππππ = πΏ0 π π‘πππ π = π Γ π π‘ππππ 1πΉ π₯π₯ = πΏ ππ΄ 0 1πΉ π₯π = π π΅π΄ 0
Chapter 6: Uniform Circular Motion and Gravitation π₯π π 2π πππ = 360Β° = 1 πππ£πππ’π‘πππ π₯π π= π₯π‘ π₯π =
π£ = ππ π£2 ππΆ = π ππΆ = ππ2 πΉπΆ = πππΆ ππ£ 2 πΉπΆ = π π£2 π‘ππ π = ππ πΉπΆ = πππ2 ππ πΉ=πΊ 2 π πΊπ π= 2 π π12 π13 = π22 π23 4π 2 3 π2 = π πΊπ π3 πΊ = π π 2 4π 2
Chapter 7: Work, Energy, and Energy Resources π = ππ πππ π 1 πΎπΈ = ππ£ 2 2 1 1 ππππ‘ = ππ£π2 β ππ£02 2 2 ππΈπ = ππβ 1 ππΈπ = ππ₯ 2 2 πΎπΈ0 + ππΈ0 = πΎπΈπ + ππΈπ πΎπΈ0 + ππΈ0 + πππ = πΎπΈπ + ππΈπ πππ’π‘ πΈππ = πΈππ π π= π‘
Chapter 8: Linear Momentum and Collisions π = ππ£ π₯π = πΉπππ‘ π₯π‘ π0 = ππ π1 π£01 + π2 π£02 = π1 π£π1 + π2 π£π2
Please Do Not Write on This Sheet Thin rod about axis through center
1 1 2 2 π1 π£01 + π2 π£02 2 2 1 2 = π1 π£π1 2 1 2 + π2 π£π2 2 π1 π£1 = π1 π£1β² πππ π1 + π2 π£2β² πππ π2 0 = π1 π£1β² π ππ π1 + π2 π£2β² π ππ π2 1 1 1 ππ£12 = ππ£1β²2 + ππ£2β²2 2 2 2 + ππ£1β² π£2β² πππ (π1 β π2 ) π£π π₯π π= βπ π π₯π‘ π£1 π1 + π£2 π2 π£ππ = π1 + π2
Chapter 9: Statics and Torque
π₯π π₯π‘ π£ = ππ π₯π πΌ= π₯π‘ π₯π£ ππ‘ = π₯π‘ ππ‘ = ππΌ π = ππ‘ π = π0 + πΌπ‘ 1 π = π0 π‘ + πΌπ‘ 2 2 π2 = π02 + 2πΌπ π0 + π π= 2 πππ‘ π = πΌπΌ Hoop about cylinder axis: πΌ = ππ
2 π=
Hoop about any diameter: πΌ = π 2
ππ
2 2
(π
12 + π
22 )
Solid cylinder (or disk) about cylinder axis: πΌ =
ππ
2 2
Solid cylinder (or disk) about central diameter: πΌ =
ππ
2 4
+
πβ2 12
1 = π2 + ππ£22 2 + ππβ2
12
β₯ to length: πΌ = Solid sphere: πΌ =
πβ2 3 2ππ
2 5
Thin spherical shell: πΌ =
2ππ
2 3
Slab about β₯ axis through center: πΌ=
π(π2 +π 2 ) 12
πππ‘ π = (πππ‘ π)π 1 πΎπΈπππ‘ = πΌπ2 2 πΏ = πΌπ π₯πΏ πππ‘ π = π₯π‘
π π πΉ π= π΄ πππ‘π = 1.01 Γ 105 ππ π = ππβ π2 = π1 + ππβ πΉ1 πΉ2 = π΄1 π΄2 πΉπ΅ = π€ππ ππππ πΉππππ‘πππ π π’πππππππ = πππ π π πππππππ ππππ£ππ‘π¦ = ππ€ πΉ πΎ= πΏ 4πΎ π= π 2πΎ πππ π β= πππ π=
Chapter 10: Rotational Motion and Angular Momentum
1 π1 + ππ£12 + ππβ1 2
Thin rod about axis through one end
Chapter 11: Fluid Statics
π = ππΉ π ππ π πβ₯ = π π ππ π πΉπ ππ ππ΄ = = πΉπ ππ ππ πΉπ = ππ πΉπ
Ring: πΌ =
β₯ to length: πΌ =
πβ2
Chapter 12: Fluid Dynamics and Its Biological Medical Applications π π= π‘ π = π΄π£ π΄1 π£1 = π΄2 π£2 π1 π΄1 π£1 = π2 π΄2 π£2
1 (Ξπ + Ξ ππ£ 2 + Ξππβ) π = πππ€ππ 2 π£1 = β2πβ πΉπΏ π= π£π΄ π2 β π1 π= π
8ππ π
= 4 ππ (π2 β π1 )ππ 4 π= 8ππ 2ππ£π ππ
= π ππ£πΏ ππ
β² = π π₯πππ = β2π·π‘
Chapter 13: Temperature, Kinetic Theory, and the Gas Laws 9 π(Β°πΆ) + 32 5 π(πΎ) = π(Β°πΆ) + 273.15 π₯πΏ = πΌπΏπ₯π π₯π΄ = 2πΌπ΄π₯π π₯π = π½ππ₯π π½ β 3πΌ ππ = πππ π = 1.38 Γ 10β23 π½/πΎ ππ΄ = 6.02 Γ 1023 πππ β1 ππ = ππ
π π½ π
= 8.31 πππ β
πΎ 1 2 ππ = πππ£ 3 1 3 2 πΎπΈ = ππ£ = ππ 2 2 π(Β°πΉ) =
π£πππ = β
3ππ π
% πππππ‘ππ£π βπ’πππππ‘π¦ π£ππππ ππππ ππ‘π¦ = π ππ‘π’πππ‘πππ π£ππππ πππππ ππ‘π¦ Γ 100%
Chapter 14: Heat and Heat Transfer Methods
1.000 ππππ = 4186 π½ π = πππ₯π π = ππΏπ π = ππΏπ£ π ππ΄(π2 β π1 ) = π‘ π π = πππ΄π 4 π‘ π½ π = 5.67 Γ 10β8 π β
π2 β
πΎ 4 ππππ‘ = πππ΄(π24 β π14 ) π‘
Chapter 15: Thermodynamics 3 π = πππ 2 π₯π = π β π π = ππ₯π (ππ ππππππ ππππππ π ) Ξπ = π β πΞπ π = 0 (ππ ππβππππ ππππππ π ) Ξπ = π π = π (ππ ππ‘βπππππ ππππππ π ) Ξπ = 0 π = 0 (πππππππ‘ππ ππππππ π ) Ξπ = βπ π πΈππ = πβ ππ (ππ¦ππππππ ππππππ π ) πΈππ = 1 β πβ ππ πΈπππΆ = 1 β πβ πβ πΆππβπ = π ππ πΆπππππ = πΆππβπ β 1 = π ππ βπ‘1 πΈπΈπ
= πβ βπ‘2 π π₯π = π πβ ππ π₯ππ‘ππ‘ = + =0 πβ ππ ππ’πππ£πππ = π₯π β
π0 π = π ππ π π = 1.38 Γ 10β23 π½/πΎ
Chapter 16: Oscillatory Motion and Waves 1 π= π π π£ = = ππ π πΉ = βππ₯
Please Do Not Write on This Sheet 1 ππΈππ = ππ₯ 2 2 π π = 2πβ π
ππΈ π π₯ππΈ = ππ₯π π = πππ΄π΅ ππ΄π΅ πΈ= π π₯π πΈ=β π₯π ππ π= π π πΆ= π π΄ πΆ = π0 π π=
1 π β 2π π
π=
2ππ‘ π₯(π‘) = π πππ ( ) π 2ππ‘ π£(π‘) = βπ£πππ₯ π ππ ( ) π π£πππ₯ =
2ππ π = πβ π π
π(π‘) = β
ππ 2ππ‘ πππ ( ) π π
π£π π‘ππππ
π0 = 8.85 Γ 10β12
πΉ =β π/πΏ
π π π£π€ = (331 ) β π 273 πΎ π πΌ= π΄ π΄π πβπππ = 4ππ 2 (π₯π)2 πΌ= 2ππ£π€
Chapter 17: Physics of Hearing πΌ π½ = (10 ππ΅) πππ ( ) πΌ0 π£π€ Β± π£π ππ = ππ ( ) π£π€ β π£π ππ΅ = |π1 β π2 | π£π€ ππ = π ( ) 2πΏ π£π€ ππ = π ( ) 4πΏ π = ππ£ (π2 β π1 )2 π= (π1 + π2 )2
Chapter 18: Electric Charge and Electric Field |ππ | = 1.60 Γ 10β19 πΆ |π1 π2 | πΉ=π π2 πΈ = πΉ/π |π| πΈ=π 2 π
Chapter 19: Electric Potential and Electric Energy
πΉ π
π΄ π ππ πΆπ 2 π2 = = = 2 2 2πΆ πΆ = π
π0
πΈπππ
Chapter 20: Electric Current, Resistance, and Ohmβs Law π₯π π₯π‘ πΌ = πππ΄π£π π = πΌπ
ππΏ π
= π΄ π = π0 (1 + πΌπ₯π) π
= π
0 (1 + πΌπ₯π) π2 π = πΌπ = = πΌ2 π
π
1 πππ£π = πΌ0 π0 2 πΌ0 πΌπππ = β2 π0 ππππ = β2 πΌ=
Chapter 21: Circuits, Bioelectricity, and DC Instruments π
π = π
1 + π
2 + π
3 + β― 1 1 1 1 = + + +β― π
π π
1 π
2 π
3 π = πππ β πΌπ π‘
π = πππ (1 β π βπ
πΆ ) π = π
πΆ π‘
π = π0 π βππΆ
Chapter 22: Magnetism πΉ = ππ£π΅ π ππ π ππ£ π= ππ΅ π = π΅ππ£ πΉ = πΌπΏπ΅ π ππ π π = ππΌπ΄π΅ π ππ π π0 πΌ π΅= 2ππ π0 πΌ π΅= 2π
π΅ = π0 ππΌ πΉ π0 πΌ1 πΌ2 = π 2ππ
Chapter 23: Electromagnetic Induction, AC Circuits, and Electrical Technologies π· = π΅π΄ πππ π π₯π· πππ = βπ π₯π‘ πππ = π£π΅πΏ πππ = ππ΄π΅π π ππ ππ‘ ππ ππ πΌπ = = ππ ππ πΌπ π₯πΌ2 πππ1 = βπ π₯π‘ π₯πΌ πππ = βπΏ π₯π‘ π₯π· πΏ=π π₯πΌ ΞΌ0 π 2 π΄ πΏ= β 1 2 πΈπππ = πΏπΌ 2 πΌ = πΌ0 (1 β π=
π‘ π βπ )
πΏ π
Please Do Not Write on This Sheet π
πππ π = π πππ£π = πΌπππ ππππ πππ π
Chapter 24: Electromagnetic Waves π=
1 βπ 0 π0
πΈ =π π΅ π = ππ ππ0 πΈ02 πΌππ£π = 2 ππ΅02 πΌππ£π = 2π0 πΈ0 π΅0 πΌπππ = 2π0
Chapter 25: Geometric Optics ππ = ππ π π= π£ π1 π ππ π1 = π2 π ππ π2 π2 ππ = π ππβ1 π1 1 π= π 1 1 1 = + π ππ ππ βπ ππ π= =β βπ ππ π
π= 2
π‘
Chapter 28: Special Relativity π₯π‘ =
πΎ=
Chapter 27: Wave Optics ππ =
π π
sin π = π
π π
2
β1 β π£2 π 1 2
β1 β π£2 π
π£2 π2 π£πΏπ + π£ππΊ π£πΏπΊ = π£ π£ 1 + πΏπ 2 ππΊ π π’ 1+ π ππππ = ππ β π’ 1β π π’ π π’ 1+ π ππ£
ππππ = ππ β π=
1 1 + ππ ππ π = ππ ππ ππ΄ = π π ππ πΌ π 1 π/# = β π· 2ππ΄ ππ = ππ ππ π= ππ
π₯π‘0
πΏ = πΏ0 β1 β
Chapter 26: Vision and Optical Instruments π=
πΌ = πΌ0 π βπ π πΌ= ππΏ ππΏ = 2πππΏ π πΌ= ππΆ 1 ππΆ = 2πππΆ π0 ππππ πΌ0 = ππ πΌπππ = π π π = βπ
2 + (ππΏ β ππΆ )2 1 π0 = 2πβπΏπΆ
1 π π ππ π = (π + ) 2 π π π ππ π = π π π π = 1.22 π· ππ 2π‘ = 2 2π‘ = ππ I = Β½ I0 πΌ = πΌ0 πππ 2 π π2 π‘ππ ππ = π1
πΈ=
1β
2
β1 β π£2 π 2 ππ
2
β1 β π£2 π πΈ0 = ππ 2 ππ 2 πΎπΈπππ = β ππ 2 2 β1 β π£2 π 2 2 πΈ = (ππ) + (ππ 2 )2