Grade 12 Physics Formula Sheet

SPH4U - Grade 12 Physics Formula Sheet General Stuff 𝑎 𝑠𝑖𝑛𝐴 = 𝑏 = 𝑠𝑖𝑛𝐵 𝑐 −𝑏±√𝑏2 −4𝑎𝑐 𝑎2 = 𝑏 2 + 𝑐 2 − 2(𝑏)(𝑐)𝑐𝑜𝑠𝐴 𝑠𝑖𝑛𝐶 2𝑎 Kinematics ⃗ avg = v ⃗ ⃗df − ⃗d𝑖 ∆d = ∆t 𝑡f − 𝑡𝑖 a⃗avg = ∆v ⃗ 𝑣f − 𝑣𝑖 = ∆t 𝑡f − 𝑡𝑖 ∆𝑑 = (𝑣f + 𝑣𝑖 ) ∆𝑡 2 𝑣f = 𝑣𝑖 + 𝑎∆𝑡 (𝑣f )2 = (𝑣𝑖 )2 + 2a⃗∆d m a⃗g = 9.8 2 [𝑑𝑜𝑤𝑛] s 1 ⃗ = 𝑣𝑖 ∆t + ⃗a(∆t)2 ∆d 2 1 ⃗ = 𝑣f ∆t − ⃗a(∆t)2 ∆d 2 Dynamics 𝐹𝑛𝑒𝑡 = 𝑚a⃗ 𝐹𝑔 = 𝑚g ⃗ 𝐹𝑓 = 𝜇𝑓 𝐹𝑁 Uniform Circular Motion 𝑣2 𝑎𝑐 = 𝑟 ⃗⃗⃗⃗ 𝑎𝑐 = 4𝜋 2 𝑟𝑓 2 ⃗⃗⃗⃗ ∑ 𝐹 = 𝑚𝑎 ⃗⃗⃗⃗𝑐 𝐹𝑐 = 𝑎𝑐 = ⃗⃗⃗⃗ 4𝜋 2 𝑟 𝑣= 𝑇2 2𝜋𝑟 𝑇 𝑚𝑣 2 𝑟 Work & Energy 𝑊 = 𝐹 ∆𝑑𝑐𝑜𝑠𝜃 1 𝐸𝑒 = 2 𝑘∆𝑥 2 1 W = E ∆𝐸𝑘 = 2 𝑚𝑣 2 𝐹𝑥 = 𝑘∆𝑥 𝑇 = 2𝜋√ 𝑘 𝑊 ∆𝐸𝑔 = 𝑚𝑔∆ℎ 𝑃 = ∆𝑡 𝑚 Momentum & Collisions 𝑝⃑ = 𝑚𝑣⃑ ∆𝑝 = 𝐹 ∆𝑡 𝑚1 𝑣𝑖1 + 𝑚2 𝑣𝑖2 = 𝑚1 𝑣𝑓1 + 𝑚2 𝑣𝑓2 𝑣𝑓 = 1 2 1 2 2 1 2 ⃗ 𝑖1 +𝑚2 𝑣 ⃗ 𝑖2 𝑚1 𝑣 𝑚1 +𝑚2 𝑚 −𝑚 2𝑚 1 1 2 𝑣𝑓1 = (𝑚1 +𝑚2 ) 𝑣𝑖1 + (𝑚 +𝑚 ) 𝑣𝑖2 2 𝑚 −𝑚 𝑣𝑓1 = (𝑚1 +𝑚2 ) 𝑣𝑖1 1 2 2 1 𝑚1 𝑣𝑖1 + 2 𝑚2 𝑣𝑖2 = 2 𝑚1 𝑣𝑓1 + 2 𝑚2 𝑣𝑓2 𝑚 −𝑚 2𝑚 1 1 1 𝑣𝑓2 = (𝑚2 +𝑚1 ) 𝑣𝑖2 + (𝑚 +𝑚 ) 𝑣𝑖1 2 2𝑚 1 𝑣𝑓2 = (𝑚 +𝑚 ) 𝑣𝑖1 1 2 2 2 Gravitational, Electric, and Magnetic Fields 𝐺 = 6.67 × 10−11 𝑁 ∙ 𝑚2 𝑘𝑔2 𝑘 = 8.99 × 109 𝑁⋅𝑚2 𝐶2 𝑚𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 = 9.11 × 10−31 𝑘𝑔 𝑚𝑝𝑟𝑜𝑡𝑜𝑛 = 1.673 × 10−27 𝑘𝑔 𝑚𝑛𝑒𝑢𝑡𝑟𝑜𝑛 = 1.675 × 10−27 𝑘𝑔 𝑒 = 1.602 × 10−19 𝐶 1 𝑒𝑉 = 1.602 × 10−19 𝐽 1𝐶 = 6.2 × 1018 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 𝐹𝑔 = 𝐺𝑚𝑝 𝐺𝑚1 𝑚2 𝑔 = 𝑟2 𝑟2 𝐺𝑚𝑝 𝑣=√ 𝑟 𝑘𝑞1 𝑞2 7.2 I 7.3 𝐹𝐸 = 𝐹𝐸 = 𝑞𝜀 𝜀 = 𝑟 22 7.4 ∆𝐸𝐸 = −𝑞𝜀∆𝑑 𝑉 = 𝑞𝐸 7.5 𝑉= 𝑟2 𝑘𝑞 𝐸 𝑘𝑞∆𝑑 𝑉= 𝑟2 ∆𝐸𝐸 ∆𝑉 = 𝑘𝑞 𝑘𝑞1 𝑞2 𝐸𝐸 = 𝑟 ∆𝑉 𝜀 = − ∆𝑑 𝑞 ∆𝐸𝐸 = 𝐸𝐸𝑓 − 𝐸𝐸𝑖 𝑟 ∆𝐸𝐸 = 𝐹𝑀 = 𝑞𝑣𝐵 𝑠𝑖𝑛 𝜃 𝑞∙ 𝑁 𝐹𝑀 = 𝐼𝐿𝐵 𝑠𝑖𝑛 𝜃 𝐼 = ∆𝑡 𝑘𝑞1 𝑞2 𝑟𝑓 − 𝑘𝑞1 𝑞2 𝑟𝑖 𝑞 = 𝑁𝑒 The Wave Nature of Light c = 3.00 × 108 𝑚 𝑠 1 𝑣 = 𝑓𝜆 𝑓=𝑇 𝑛1 𝑠𝑖𝑛 𝜃1 = 𝑛2 𝑠𝑖𝑛 𝜃2 1 9.3 |𝑃𝑛 𝑆1 − 𝑃𝑛 𝑆2 | = (𝑛 − ) 𝜆 9.5 𝑠𝑖𝑛 𝜃𝑚 = 𝑑 𝑠𝑖𝑛 𝜃𝑛 = 2 𝑚𝜆 𝑥𝑛 = 𝑑 1 2 (𝑚+ )𝜆 2𝑡 = 𝑛 10.1 𝑓𝑖𝑙𝑚 𝑠𝑖𝑛 𝜃𝑚 = 10.2 𝑦𝑚 = 1 2 𝑤 1 2 (𝑚+ )𝐿𝜆 𝑤 1 2 (𝑛− )𝜆 𝜆 𝑛 = 𝜆1 𝑠𝑖𝑛𝜃𝑐 = 𝑛2 2 1 𝑥𝑛 𝑥𝑛 𝑠𝑖𝑛 𝜃𝑛 = 𝐿 𝑑 𝐿 = 1 2 𝑑 𝑛𝜆 𝐿𝜆 𝛥𝑥 = 𝑑 𝜆 𝛥𝑥 = 𝐿 (2𝑡) 𝑛𝜆 𝑠𝑖𝑛 𝜃𝑛 = 𝑤 𝑛𝐿𝜆 𝐿𝜆 𝑦𝑛 = 𝑤 𝛥𝑦 = 𝑤 1 𝑑=𝑁 10.3 Revolutions in Modern Physics: Quantum Mechanics & Special Relativity 1𝑒𝑉 = 1.602 × 10−19 𝐽 𝛥𝑡𝑚 = 𝛥𝑡𝑠 2 √1−𝑣2 𝑐 𝐸𝑡𝑜𝑡𝑎𝑙 = 𝑚𝑐 2 2 √1−𝑣2 𝑐 𝑣2 𝑝= 𝐸𝑟𝑒𝑠𝑡 = 𝑚𝑐 2 𝐸𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ𝑓 = 𝜆 ℎ𝑓 ℎ = 𝑐 𝜆 𝑚𝑣 2 √1−𝑣2 𝑐 𝑚𝑚 = 𝑚𝑠 2 √1−𝑣2 𝑐 𝐸𝑡𝑜𝑡𝑎𝑙 = 𝐸𝐾 + 𝐸𝑟𝑒𝑠𝑡 ℎ𝑐 𝑊 = 𝑒∆𝑉 𝑝𝑝ℎ𝑜𝑡𝑜𝑛 = ℎ = 6.63 × 10−34 𝐽 ∙ 𝑠 𝐿𝑚 = 𝐿𝑠 √1 − 𝑐 2 𝐸𝑘 = ℎ𝑓 − ℎ𝑓0 1 2 (𝑛− )𝜆 𝑑 𝑓𝑖𝑙𝑚 (𝑚+ )𝜆 2 𝑛1 1 2 (𝑛− )𝐿𝜆 2𝑡 = 𝑛 𝑛2 (𝑛− )𝜆 𝑠𝑖𝑛 𝜃𝑛 = 𝑚𝐿𝜆 𝑥𝑚 = 𝜆 𝑛 = 𝜆1 𝐸𝑘 = ℎ𝑓 − 𝑊 𝑑

Grade 12 Physics Formula Sheet

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Grade 12 Physics Formula Sheet

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