Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 1
Haroldโs AP Physics โCheat Sheetโ 24 March 2017
Mechanics:
Linear Translation
Mechanics: Angular / Rotational
Motion
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Kinematics
Position (m)
(rad)
Horizontal:
๐ = ๐ฅ0 + ๐ฃ๐ฅ0๐ก +1
2๐๐ก2
Vertical:
๐ = ๐ฆ0 + ๐ฃ๐ฆ0๐ก โ1
2๐๐ก2
๐ = ๐ฅ0 + ๐๐ก
๐ = ๐๐
๐ฅ = โซ๐ฃ ๐๐ก
๐ = ๐0 +๐0๐ก +1
2๐ถ๐ก2
๐ฅ = ๐ด cos(๐๐ก)
๐ฅ = ๐ด cos(2๐๐๐ก)
10โ24 = ๐ฆ๐๐๐ก๐ยญ 10โ21 = ๐ง๐๐๐ก๐ยญ 10โ18 = ๐๐ก๐ก๐ยญ 10โ15 = ๐๐๐๐ก๐ยญ 10โ12 = ๐๐๐๐ยญ 10โ9 = ๐๐๐๐ยญ 10โ6 = ๐๐๐๐๐ยญ 10โ3 = ๐๐๐๐๐ยญ 100 = 1 103 = ๐๐๐๐ยญ 106 = ๐๐๐๐ยญ 109 = ๐๐๐๐ยญ 1012 = ๐ก๐๐๐ยญ 1015 = ๐๐๐ก๐ยญ 1018 = ๐๐ฅ๐ยญ 1021 = ๐ง๐๐ก๐ก๐ยญ 1024 = ๐ฆ๐๐ก๐ก๐ยญ
Fluid Mechanics:
๐1 + ๐๐๐ฆ1 +1
2๐๐ฃ1
2
= ๐2 + ๐๐๐ฆ2 +1
2๐๐ฃ2
2
(Conservation of Mass)
๐ =๐
๐
โโ = ๐ผโ0โ๐
Waves and Optics: 1
๐ ๐+1
๐ ๐=1
๐
โ๐ฟ = ๐๐
๐ sin๐ = ๐๐
Relativity:
๐ฟ = ๐ฟ0โ1โ๐ฃ2
๐2
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 2
Velocity (m/s)
(rad/s)
๐ =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
๐ = ๐0 + ๐๐ก
๐2 = ๐ฃ0
2 + 2๐(๐ฅ โ ๐ฅ0)
๏ฟฝฬ ๏ฟฝ =๐ฃ0 + ๐ฃ
2
๐ = ๐๐ ๐ = ๐ ร ๐
๐ฃ = โซ๐๐๐ก
๐ =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
๐ = ๐0 + ๐ถ๐ก
๐2 = ๐0
2 + 2๐ถ(๐ โ ๐0)
๏ฟฝฬ ๏ฟฝ =๐0 +๐
2
๐ =2๐
๐= 2๐๐
๐ = โ๐
๐= โ
๐
โ
Speed of Light:
๐ โ 3.00 ๐ฅ 108 ๐
๐
= 299,792,458 ๐
๐
Fluid Mechanics: ๐ด1๐ฃ1 = ๐ด2๐ฃ2
๐ฃ๐๐๐ = โ3๐ ๐
๐
๐ฃ๐๐๐ = โ3๐๐ต๐
๐
Waves and Optics: ๐ฃ = ๐๐
๐ =๐
๐ฃ
๐1 sin๐1 = ๐2 sin๐2
Relativity:
๐ฃ(๐ก) = ๐ฃ0
โ1 โ๐ฃ2
๐2
Acceleration
(m/๐๐) (rad/๐ 2)
๐ =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
๐ =โ๐ญ
๐=๐ญ๐๐๐ก๐
๐ = ๐๐ถ
๐ = 9.80665 ๐
๐ 2
๐ = 32.1740 ๐๐ก
๐ 2
Tangential:
๐ถ = ๐๐๐=โ๐
โ๐ก=๐๐
๐๐ก
๐ถ =โ๐
๐ผ=๐๐๐๐ก๐ผ
Centripetal:
๐๐ = ๐2
๐= ๐2๐
๐2 = ๐๐
2 + ๐๐2
NA NA NA
Jerk (Jolt) (m/๐๐)
(rad/๐ 3)
๐ =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
๐ =๐ถ
๐ก=โ๐ถ
โ๐ก=๐๐ถ
๐๐ก NA NA NA
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 3
Dynamics
Mass (kg)
/ Moment of
Inertia (๐๐ โข๐2)
m = actual mass I = effective mass
๐ผ =โ๐๐2
๐ผ = โซ๐2 ๐๐
๐ผ = โซ๐ โข ๐๐
๐๐= 9.11 ร10โ31 ๐๐
๐๐ โ ๐๐= 1.67 ร10โ27 ๐๐
NA
Relativity:
๐ =๐0
โ1 โ๐ฃ2
๐2
Momentum (kgโขm/s)
(๐๐ โข๐2/๐ )
๐ = ๐๐
โ๐ = ๐โ๐
Conservation of Momentum: ๐๐ = ๐๐
๐ณ = ๐ผ๐
๐ณ = ๐ ร ๐
๐ฟ = โซ๐ ร ๐ ๐๐
NA Fluid Mechanics:
๐ป๐ = ๐๐
Atomic and Nuclear:
๐ =โ
๐
Relativity:
๐ =๐๐ฃ
โ1 โ๐ฃ2
๐2
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 4
Force (N =
kgโขm/๐๐) /
Torque (J = Nโขm)
๐ญ = ๐๐
๐ญ๐ = ๐๐
โ๐ญ = ๐ญ๐๐๐ก = ๐๐
๐ญ =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
๐ญ๐๐๐๐ โค ๐๐
Hookeโs Law: ๐ญ๐ = โ๐๐
๐น๐บ = โ๐บ๐1๐2๐2
๐ญ๐บ = โ๐บ๐1๐2๐2
๏ฟฝฬ๏ฟฝ
๐ = ๐๐น sin๐
โ๐ = ๐๐๐๐ก = ๐ผ๐ถ
๐ = ๐๐น = ๐ผ๐ถ
๐ = ๐ ร ๐ญ
๐ =๐๐ฟ
๐๐ก
๐ญ = ๐๐๐
๐ญ =๐๐2
๐
๐ญ = ๐๐๐2
Electricity: Coulombโs Law:
๐น = ๐๐1๐2๐2
๐น =1
4๐๐0 ๐1๐2๐2
๐ญ = ๐ฌ๐
Magnetism: ๐น๐ต = ๐๐ฃ๐ต sin ๐
๐น๐ต = ๐ต๐ผโ sin๐
๐ญ๐ต = ๐๐ ร ๐ฉ
๐ญ๐ต = ๐ผโ ร ๐ฉ
๐ญ = โซ๐ผ ๐โร ๐ฉ
Fluid Mechanics: ๐น = ๐๐ด
๐ =๐น
๐ด= ๐โ๐
๐น๐๐ข๐๐ฆ = ๐๐๐
๐๐ = ๐๐ ๐ = ๐๐๐ต๐
๐ = 8.31๐ฝ
(๐๐๐ โข ๐พ)
๐๐ต = 1.38 ร10โ23
๐ฝ
๐พ
NA
Impulse (Nโขs)
(Nโขmโขs)
๐ฑ = ๐ญ โ๐ก = โ๐ = ๐ โ๐
๐ฑ = โซ๐ญ ๐๐ก = โ๐
๐ฏ = ๐ โ๐ก = โ๐ณ = ๐ฐ โ๐
๐ฏ = โซ๐ ๐๐ก = โ๐ณ
NA NA NA
Yank (N/๐๐)
Rotatum (J/s)
๐ = ๐ ๐ฑ
๐ =๐ญ
๐ก=โ๐น
โ๐ก=๐๐ญ
๐๐ก
๐ท = ๐ ร ๐
๐ท =๐
๐ก=โ๐
โ๐ก=๐๐
๐๐ก
NA NA NA
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 5
Energy
Work (J = Nโขm)
๐ = ๐น๐
๐ = ๐น โ๐ฅ cos ๐
๐ = โซ๐ญ โข ๐๐
๐ = ๐ โ๐
๐ = ๐ (๐ โ ๐0)
๐ = โซ๐ โข ๐๐ฝ
๐พ = ๐ธ๐
Thermodynamics: ๐ = โ๐ โ๐
๐ = |๐
๐๐ป|
๐๐ =๐๐ป โ ๐๐ถ๐๐ป
NA
Kinetic Energy
(J) ๐พ =
1
2๐๐2 ๐พ =
1
2๐ผ๐2
1 ๐๐= 1.60 ร10โ19 ๐ฝ
Fluid Mechanics:
๐ + ๐๐๐ฆ +1
2๐๐ฃ2
= ๐๐๐๐ ๐ก๐๐๐ก
Thermodynamics:
๐พ๐๐ฃ๐ =3
2๐๐ต๐
Atomic and Nuclear: ๐พ๐๐๐ฅ = โ๐ โ ๐
Relativity: ๐พ =
๐0๐2
(
1
โ1 โ๐ฃ2
๐2
โ 1
)
Potential Energy
(J)
โ๐๐ = ๐๐โ
๐๐บ = โ๐บ๐1๐2๐
๐บ = 6.67 ร10โ11
Coiled spring:
๐๐ = โ1
2๐๐ฅ2
๐๐ธ = ๐๐
๐๐ธ =1
4๐๐0 ๐1๐2๐
๐๐ =1
2๐๐
๐๐ =1
2๐ถ๐2
๐๐ฟ =1
2๐ฟ๐ผ2
Fluid Mechanics: ๐ = ๐0 + ๐๐โ
Thermodynamics: โ๐ = ๐ +๐
Atomic and Nuclear: ๐ธ = โ๐ = ๐๐
๐ธ = ๐๐2
โ๐ธ = (โ๐)๐2
Relativity:
๐ธ = ๐๐2
(
1
โ1 โ๐ฃ2
๐2)
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 6
Heat Energy
(J)
Conservation of Energy: ๐ฌ๐ = ๐ฌ๐
๐ธ= ๐ + ๐ + ๐พ + โ๐๐+ ๐๐บ + ๐๐ + ๐๐ธ + ๐๐+ ๐๐ฟ +โฏ = ๐๐๐๐ ๐ก๐๐๐ก
NA NA
Thermodynamics:
๐ป =๐๐ดโ๐
๐ฟ
๐ = ๐๐ป๐
๐ = ๐๐ป๐ฃ
โ๐ธ = ๐ = ๐๐ถโ๐
๐๐ถโ๐ = ๐๐ถ(๐๐ โ ๐๐)
๐ถ๐ป2๐ = 4180 ๐ฝ/Kg ยฐK
๐๐
=๐1๐ถ1โ๐1๐ +๐2๐ถ2โ๐2๐
๐1๐ถ1 +๐2๐ถ2
NA
Power (W)
๐ =๐
โ๐ก= ๐น๐ฃ
๐ =โ๐ธ
โ๐ก=๐๐ธ
๐๐ก
๐ = ๐น๐ฃ cos ๐
๐ = ๐ญ โข ๐
๐ =๐
โ๐ก= ๐๐
๐ =โ๐
โ๐ก=๐๐
๐๐ก
๐ = ๐๐ cos ๐
๐ = ๐ โข ๐
๐ = ๐ผ๐
๐ = ๐ผ2๐
๐ =๐2
๐
NA NA
Mechanics: Linear
Mechanics: Angular
Electricity / Magnetism
Fluid Mechanics /
Thermo-dynamics
Atomic and Nuclear /
Waves and Optics
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 7
Engineering Application
Period / Frequency
(Hz)
๐ =1
๐
๐ =1
๐
๐ =1
๐=2๐
๐
๐๐ = 2๐โ๐
๐
๐๐ = 2๐โโ
๐
๐ =2๐
๐
For: ๐ฆ = ๐ ๐๐(๐๐) ๐ฆ = ๐๐๐ (๐๐)
NA
Waves and Optics:
๐ =๐
๐ฃ
Doppler Effect:
๐๐ = ๐๐ (๐ ยฑ ๐๐๐ โ ๐๐
)
Relativity:
๐ก = ๐ก0
โ1 โ๐ฃ2
๐2
Center of Mass
(m)
๐ฅ๐ถ๐ =๐1๐ฅ1 +๐2๐ฅ2๐1 +๐2
๐ฅ๐ถ๐ =โ๐๐๐ฅ๐โ๐๐
๏ฟฝฬ ๏ฟฝ =1
๐ โซ ๐ฅ ๐๐
๐
0
where ๐ = โซ ๐๐๐
0
and ๐๐ = ๐ ๐๐ง ๐๐ฆ ๐๐ฅ
๐๐ถ๐ =โ๐๐
โ๐ NA NA
Waves and Optics:
|๐| = |โ๐โ๐| = |
๐ ๐๐ ๐|
(magnification)
Rigid Bodies
โ๐น๐ฆ =โ๐๐ =0
(Down = โโโ)
โ๐ =โ๐น๐ฆ๐ฅ๐ถ๐ = 0
(CW = โโโ)
Conservation of Charge
Conservation of Mass Conservation of
Energy
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 8
Electricity Electricity
Electric Field
(V/m) (N/C)
๐ฌ =๐ญ
๐
๐ธ๐๐ฃ๐ = โ๐
๐
๐ธ = โโ๐
โ๐= โ
๐๐
๐๐
Gaussโs Law:
โฎ๐ฌ โข ๐๐จ =๐
๐0
๐ฌ = ๐๐ฑ
Capacitance (F)
๐ถ =๐
๐
๐ถ =๐0๐ด
๐
๐ถ =๐ ๐0๐ด
๐
๐ถ๐ = โ ๐ถ๐๐
1
๐ถ๐ = โ
1
๐ถ๐๐
Potential (V)
๐ = ๐ผ๐
๐ =๐
๐ถ
๐ = ๐โ๐๐๐๐๐
๐ =1
4๐๐0โ
๐๐๐๐๐
Resistance (ฮฉ)
๐ =๐
๐ผ
๐ =๐โ
๐ด
๐ ๐ = โ ๐ ๐๐
1
๐ ๐= โ
1
๐ ๐๐
Current (A)
๐ผ๐๐ฃ๐ =โ๐
โ๐ก
๐ผ =๐๐
๐๐ก
๐ผ =๐
๐
๐ผ = ๐๐๐ฃ๐๐ด
๐ = 1.60 ร10โ19 ๐ถ
EMF (V)
Faradayโs Law of Induction:
โฎ๐ฌ โข ๐๐ต = โ โ๐๐ตโ๐ก
๐ = โ๐ฟ๐๐ผ
๐๐ก
Copyright ยฉ 2011-2017 by Harold Toomey, WyzAnt Tutor 9
Magnetism Magnetism
Magnetic Field (T)
๐ต =๐02๐ ๐ผ
๐
๐๐๐๐๐๐๐๐: ๐ต๐ = ๐0๐๐ผ
๐คโ๐๐๐ ๐ =๐
๐ต ๐ก๐ข๐๐๐ ๐๐๐ ๐๐๐ก๐๐
๐ฉ =๐04๐ ๐๏ฟฝโโโ๏ฟฝ ร ๏ฟฝโโ๏ฟฝ
๐3
๐ฉ =๐04๐ ๐๏ฟฝโโโ๏ฟฝ ร ๏ฟฝฬ๏ฟฝ
๐2
๐0 = 4๐ ร10โ7(๐ โข ๐)
๐ด
Ampereโs Circuit Law:
โฎ๐ฉ โข ๐๐ต = ๐๐๐ผ
๐๐ต =๐04๐ ๐ผ ๐๐ต ร ๏ฟฝโโ๏ฟฝ
๐3
Magnetic Flux (Wb)
๐๐ฉ = ๐ต๐ด cos ๐
๐๐ต = ๐ฉ โข ๐จ
Gaussโs Law for Magnetism:
๐๐ต = โซ๐ฉ โข ๐๐จ
EMF (V)
๐๐๐ฃ๐ = โ โ๐๐ตโ๐ก
๐บ = ๐ฉ๐๐ฃ