Physics 101 Formulas
12/7/2017 1
Kinematics
𝒗𝒗𝑎𝑎𝑎𝑎𝑎𝑎 = 𝛥𝛥𝒙𝒙
𝛥𝛥𝛥𝛥 𝒂𝒂𝑎𝑎𝑎𝑎𝑎𝑎 = 𝛥𝛥𝒗𝒗
𝛥𝛥𝛥𝛥
𝑣𝑣 = 𝑣𝑣0 + 𝑎𝑎𝑎𝑎 𝑥𝑥 = 𝑥𝑥0 + 𝑣𝑣0𝑎𝑎 + 1
2𝑎𝑎𝑎𝑎2
𝑣𝑣2 = 𝑣𝑣0
2 + 2𝑎𝑎𝑎𝑎𝑥𝑥
𝑔𝑔 = 9.8 m/s2 = 32.2 ft/s2 (near Earth’s surface)
Dynamics
𝛴𝛴𝑭𝑭 = 𝑚𝑚𝒂𝒂 𝑊𝑊𝑊𝑊𝑊𝑊𝑔𝑔ℎ𝑎𝑎 = 𝑚𝑚𝑔𝑔 (near Earth’s surface)
𝑓𝑓𝑠𝑠,𝑚𝑚𝑎𝑎𝑚𝑚 = 𝜇𝜇𝑠𝑠𝐹𝐹𝑁𝑁
𝑓𝑓𝑘𝑘 = 𝜇𝜇𝑘𝑘𝐹𝐹𝑁𝑁 𝑎𝑎𝑐𝑐 = 𝑎𝑎2
𝑅𝑅 = 𝜔𝜔2𝑅𝑅
Universal Gravitation
Universal Gravitational Constant 𝐺𝐺 = 6.7 × 10–11 N ∙m2
kg2
𝐹𝐹𝑔𝑔 = 𝐺𝐺𝑚𝑚1𝑚𝑚2
𝑅𝑅2 𝑈𝑈𝑔𝑔 = −𝐺𝐺𝑚𝑚1𝑚𝑚2
𝑅𝑅
Work & Energy
𝑊𝑊𝐹𝐹 = 𝐹𝐹𝐹𝐹cos(𝜃𝜃) 𝐾𝐾 = 1
2𝑚𝑚𝑣𝑣2 = 𝑝𝑝2
2𝑚𝑚 𝑊𝑊𝑁𝑁𝑁𝑁𝑁𝑁 = 𝑎𝑎𝐾𝐾 = 𝐾𝐾𝑓𝑓 – 𝐾𝐾𝑖𝑖 𝐸𝐸 = 𝐾𝐾 + 𝑈𝑈
𝑊𝑊𝑛𝑛𝑐𝑐 = 𝑎𝑎𝐸𝐸 = 𝐸𝐸𝑓𝑓 – 𝐸𝐸𝑖𝑖 = (𝐾𝐾𝑓𝑓 + 𝑈𝑈𝑓𝑓) – (𝐾𝐾𝑖𝑖 + 𝑈𝑈𝑖𝑖) 𝑈𝑈𝑔𝑔𝑔𝑔𝑎𝑎𝑎𝑎 = 𝑚𝑚𝑔𝑔𝑚𝑚
Impulse & Momentum
Impulse: 𝑰𝑰 = 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑 = 𝑚𝑚𝒗𝒗𝑓𝑓 – 𝑚𝑚𝒗𝒗𝑖𝑖 𝑭𝑭𝑎𝑎𝑎𝑎𝑎𝑎 = 𝑎𝑎𝒑𝒑/𝑎𝑎𝑎𝑎
𝛴𝛴𝑭𝑭𝑎𝑎𝑚𝑚𝛥𝛥𝑎𝑎𝑎𝑎 = 𝑎𝑎𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡 = 𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡,𝑓𝑓𝑖𝑖𝑛𝑛𝑎𝑎𝑡𝑡 – 𝑷𝑷𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡,𝑖𝑖𝑛𝑛𝑖𝑖𝛥𝛥𝑖𝑖𝑎𝑎𝑡𝑡 (momentum conserved if 𝛴𝛴𝑭𝑭𝑎𝑎𝑚𝑚𝛥𝛥 = 0)
𝒙𝒙𝑐𝑐𝑚𝑚 = 𝑚𝑚1𝒙𝒙1 + 𝑚𝑚2𝒙𝒙2
𝑚𝑚1 + 𝑚𝑚2
Elastic Collisions: Mass 𝒎𝒎𝒊𝒊 moving with 𝒗𝒗𝒊𝒊; Stationary mass 𝑴𝑴
𝑣𝑣𝑚𝑚,𝑓𝑓=𝑣𝑣𝑚𝑚,𝑖𝑖𝑚𝑚−𝑀𝑀
𝑚𝑚+𝑀𝑀 𝑣𝑣𝑀𝑀,𝑓𝑓=𝑣𝑣𝑚𝑚,𝑖𝑖2𝑚𝑚
𝑚𝑚+𝑀𝑀
Rotational Kinematics
𝜔𝜔 = 𝜔𝜔0 + 𝛼𝛼𝑎𝑎 𝜃𝜃= 𝜃𝜃0 + 𝜔𝜔0𝑎𝑎 + 1
2𝛼𝛼𝑎𝑎2 𝜔𝜔2 = 𝜔𝜔0
2 + 2𝛼𝛼𝑎𝑎𝜃𝜃
𝑎𝑎𝑥𝑥𝑁𝑁 = 𝑅𝑅𝑎𝑎𝜃𝜃 𝑣𝑣𝑁𝑁 = 𝑅𝑅𝜔𝜔 𝑎𝑎𝑁𝑁 = 𝑅𝑅𝛼𝛼
(rolling without slipping: 𝑎𝑎𝑥𝑥 = 𝑅𝑅𝑎𝑎𝜃𝜃 𝑣𝑣 = 𝑅𝑅𝜔𝜔 𝑎𝑎 = 𝑅𝑅𝛼𝛼 )
1 revolution = 2π radians
Rotational Statics & Dynamics
𝜏𝜏= 𝐹𝐹𝐹𝐹 sin 𝜃𝜃
𝛴𝛴𝜏𝜏 = 0 and 𝛴𝛴𝐹𝐹 = 0 (static equilibrium)
𝛴𝛴𝜏𝜏 = 𝐼𝐼𝛼𝛼
𝑊𝑊 = 𝜏𝜏𝜃𝜃
𝑳𝑳 = 𝐼𝐼𝝎𝝎 𝛴𝛴𝝉𝝉𝑎𝑎𝑚𝑚𝛥𝛥𝑎𝑎𝑎𝑎 = 𝑎𝑎𝑳𝑳
(angular momentum conserved if 𝑎𝑎𝝉𝝉𝑎𝑎𝑚𝑚𝛥𝛥 = 0)
𝐾𝐾𝑔𝑔𝑡𝑡𝛥𝛥 = 1
2𝐼𝐼𝜔𝜔2 = 𝐿𝐿2
2𝐼𝐼
𝐾𝐾𝛥𝛥𝑡𝑡𝛥𝛥𝑎𝑎𝑡𝑡 = 𝐾𝐾𝛥𝛥𝑔𝑔𝑎𝑎𝑛𝑛𝑠𝑠 + 𝐾𝐾𝑔𝑔𝑡𝑡𝛥𝛥 = 1
2𝑚𝑚𝑣𝑣2 + 1
2𝐼𝐼𝜔𝜔2
𝐼𝐼=𝐼𝐼𝑐𝑐𝑚𝑚 +𝑚𝑚𝐹𝐹2 Parallel axis theorem
Moments of Inertia (I)
𝐼𝐼= 𝛴𝛴𝑚𝑚𝐹𝐹2
(for a collection of point particles)
𝐼𝐼 = 1
2𝑀𝑀𝑅𝑅2 (solid disk or cylinder)
𝐼𝐼 = 2
5𝑀𝑀𝑅𝑅2 (solid ball)
𝐼𝐼 = 2
3𝑀𝑀𝑅𝑅2 (hollow sphere)
𝐼𝐼 = 𝑀𝑀𝑅𝑅2 (hoop or hollow cylinder)
𝐼𝐼 = 1
12 𝑀𝑀𝐿𝐿2 (uniform rod about center)
𝐼𝐼 =
1
3 𝑀𝑀𝐿𝐿
2
(uniform rod about one end)
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