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SPH3U – Grade 11 Physics Formula Sheet
Prefixes
πœ‚ = π‘₯ 10−9
πœ‡ = π‘₯ 10−6
π‘š = π‘₯ 10−3
π‘˜ = π‘₯ 103
𝑀 = π‘₯ 106
𝐺 = π‘₯ 109
Trigonometry
Quadratic Equation
−𝑏 ± √𝑏 2 − 4π‘Žπ‘
2π‘Ž
Right Angle Triangle (SOH CAH TOA & Pythagorean Theorem)
π‘ π‘–π‘›πœƒ =
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π‘π‘œπ‘ πœƒ =
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
β„Žπ‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π‘‘π‘Žπ‘›πœƒ =
π‘œπ‘π‘π‘œπ‘ π‘–π‘‘π‘’
π‘Žπ‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘
𝑐 2 = π‘Ž2 + 𝑏 2
Non-Right Angle Triangle (Sine & Cosine Law)
π‘Ž2 = 𝑏 2 + 𝑐 2 − 2 βˆ™ 𝑏 βˆ™ 𝑐 βˆ™ π‘π‘œπ‘ π΄
𝑏 2 = π‘Ž2 + 𝑐 2 − 2 βˆ™ π‘Ž βˆ™ 𝑐 βˆ™ π‘π‘œπ‘ π΅
𝑐 2 = π‘Ž2 + 𝑏 2 − 2 βˆ™ π‘Ž βˆ™ 𝑏 βˆ™ π‘π‘œπ‘ πΆ
π‘Ž
𝑏
𝑐
=
=
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐡 𝑠𝑖𝑛𝐢
Error
% πΈπ‘Ÿπ‘Ÿπ‘œπ‘Ÿ =
|π‘šπ‘’π‘Žπ‘ π‘’π‘Ÿπ‘’π‘‘ π‘£π‘Žπ‘™π‘’π‘’ − π‘Žπ‘π‘π‘’π‘π‘‘π‘’π‘‘ π‘£π‘Žπ‘™π‘’π‘’|
π‘₯ 100%
π‘Žπ‘π‘π‘’π‘π‘‘π‘’π‘‘ π‘£π‘Žπ‘™π‘’π‘’
% π·π‘–π‘“π‘“π‘’π‘Ÿπ‘’π‘›π‘π‘’ =
|π‘£π‘Žπ‘™π‘’π‘’1 − π‘£π‘Žπ‘™π‘’π‘’2 |
π‘₯ 100%
π‘£π‘Žπ‘™π‘’π‘’1 + π‘£π‘Žπ‘™π‘’π‘’2
(
)
2
Kinematics
βƒ— avg =
v
a⃗avg
βƒ—
βƒ—df − βƒ—d𝑖
βˆ†d
=
βˆ†t
𝑑f − 𝑑𝑖
βˆ†v
βƒ—
𝑣f − 𝑣𝑖
=
=
βˆ†t
𝑑f − 𝑑𝑖
a⃗g = 9.8
m
[π‘‘π‘œπ‘€π‘›]
s2
βˆ†π‘‘ =
(𝑣f + 𝑣𝑖 )
βˆ†π‘‘
2
𝑣f = 𝑣𝑖 + π‘Žβˆ†π‘‘
(𝑣f )2 = (𝑣𝑖 )2 + 2aβƒ—βˆ†d
1
βƒ— = 𝑣𝑖 βˆ†t + βƒ—a(βˆ†t)2
βˆ†d
2
1
βƒ— = 𝑣f βˆ†t − βƒ—a(βˆ†t)2
βˆ†d
2
Dynamics (Forces)
𝐹𝑛𝑒𝑑 = ∑ πΉπ‘œπ‘Ÿπ‘π‘’π‘ 
𝐹𝑛𝑒𝑑 = π‘šaβƒ—
𝐹𝑔 = π‘šg
βƒ—
πΉπ‘˜ = πœ‡π‘˜ 𝐹𝑁
𝐹𝑠 = πœ‡π‘  𝐹𝑁
𝐹=
πΊπ‘š1 π‘š2
𝑑2
𝑁
𝑔 = 9.8 π‘˜π‘” [π‘‘π‘œπ‘€π‘›]
𝐺 = 6.67 × 10−11
𝑁 βˆ™ π‘š2
π‘˜π‘”2
Work, Energy, Power and Society
π‘Š = 𝐹 βˆ†π‘‘π‘π‘œπ‘ πœƒ
𝑃=
βˆ†πΈ
βˆ†π‘‘
=
1
βˆ†πΈπ‘˜ = 2 π‘šπ‘£ 2
βˆ†πΈπ‘” = π‘šπ‘”βˆ†β„Ž
π‘Š
βˆ†π‘‘
𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 =
𝑄 = π‘šπ‘βˆ†π‘‡
𝑄f = π‘šπΏf
𝑇𝐾 = 𝑇𝐢 + 273
𝑑=
π‘š
𝑉
πΈπ‘œπ‘’π‘‘
𝐸𝑖𝑛
πΈπ‘š = 𝐸𝑔 + πΈπ‘˜
π‘Š = βˆ†πΈ
π‘₯ 100%
𝑄𝑣 = π‘šπΏπ‘£
π‘„π‘™π‘œπ‘ π‘‘ + π‘„π‘”π‘Žπ‘–π‘›π‘’π‘‘ = 0
 (density)
𝑑
𝐴=
1 β„Ž
𝐴0 (2)
𝐸 = π‘šπ‘ 2
π‘šπ‘’π‘™π‘’π‘π‘‘π‘Ÿπ‘œπ‘› = 9.11 × 10−31 π‘˜π‘”
π‘šπ‘π‘Ÿπ‘œπ‘‘π‘œπ‘› = 1.673 × 10−27 π‘˜π‘”
π‘šπ‘›π‘’π‘’π‘‘π‘Ÿπ‘œπ‘› = 1.675 × 10−27 π‘˜π‘”
π‘šπ‘’π‘™π‘’π‘π‘‘π‘Ÿπ‘œπ‘› = 0.000549 𝑒
π‘šπ‘π‘Ÿπ‘œπ‘‘π‘œπ‘› = 1.007276 𝑒
π‘šπ‘›π‘’π‘’π‘‘π‘Ÿπ‘œπ‘› = 1.008665 𝑒
1 𝑒 = 1.66 × 10−27 π‘˜π‘”
Waves and Sound
1
1
𝑓=𝑇
π‘š
πœ‡=
𝑓 = βˆ†π‘‘
𝐹
𝑣 = √ πœ‡π‘‡
𝐿
𝐿𝑛 =
𝑁
𝑇=𝑓
(2𝑛−1)
4
πœ†
𝐿𝑛 =
𝑇=
βˆ†π‘‘
π‘£π‘ π‘œπ‘’π‘›π‘‘ = 331.4
π‘›πœ†
π‘š
𝑠
+ (0.606
π‘š/𝑠
°πΆ
)π‘₯ 𝑇
𝑀=
π‘£π‘ π‘œπ‘’π‘›π‘‘ + π‘£π‘‘π‘’π‘‘π‘’π‘π‘‘π‘œπ‘Ÿ
π‘“π‘π‘’π‘Žπ‘‘ = |𝑓2 − 𝑓1 |
2
c = 3.00 × 108
𝑣 = π‘“πœ†
𝑁
π‘“π‘œπ‘π‘  = (
π‘£π‘ π‘œπ‘’π‘›π‘‘ + π‘£π‘ π‘œπ‘’π‘Ÿπ‘π‘’
π‘š
𝑠
π‘Žπ‘–π‘Ÿπ‘ π‘π‘’π‘’π‘‘ π‘œπ‘“ π‘œπ‘π‘—π‘’π‘π‘‘
π‘™π‘œπ‘π‘Žπ‘™ 𝑠𝑝𝑒𝑒𝑑 π‘œπ‘“ π‘ π‘œπ‘’π‘›π‘‘
) π‘“π‘ π‘œπ‘’π‘Ÿπ‘π‘’
Electricity
𝑃=
βˆ†πΈ
βˆ†π‘‘
𝑉=
βˆ†πΈ
𝑄
1π‘˜π‘Š βˆ™ β„Ž = 3.6 × 106 𝐽
𝑄
𝐼 = βˆ†π‘‘
𝑄 = 𝑁𝑒
𝑉 = 𝐼𝑅
𝑒 = 1.602 × 10−19 𝐢
1 𝑒𝑉 = 1.602 × 10−19 𝐽
Series Circuit
Parallel Circuit
VT = 𝑉1 + 𝑉2 + 𝑉3 + β‹―
𝑉T = 𝑉1 = 𝑉2 = 𝑉3 = β‹―
IT = I1 = I2 = I3 = β‹―
IT = I1 + I2 + I3 + β‹―
𝑅T = 𝑅1 + 𝑅2 + 𝑅3 + β‹―
Electromagnetism
𝑉𝑃 𝐼𝑆
𝑁𝑃
= =
𝑉𝑆 𝐼𝑃
𝑁𝑆
1
𝑅𝑇
=
1
𝑅1
+
1
𝑅2
𝑃 = 𝐼𝑉 = 𝐼 2 𝑅 =
+
1
𝑅3
+β‹―
𝑉2
𝑅
1𝐢 = 6.2 × 1018 π‘’π‘™π‘’π‘π‘‘π‘Ÿπ‘œπ‘›π‘ 
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