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Cheatsheet - Fórmulas de Física para Física General y Física de Ingenieros
- 1. 𝑣𝑓 = 𝑣𝑖 + 𝑎𝑡
𝑑 = ҧ𝑣𝑡
ҧ𝑣 =
𝑣𝑖 + 𝑣𝑓
2
𝑑 = 𝑣𝑖 𝑡 +
1
2
𝑎𝑡2
𝑑 =
𝑣𝑓
2
− 𝑣𝑖
2
2𝑎
Ԧ𝐹 = 𝑚 Ԧ𝑎
Ԧ𝐹 =
∆ Ԧ𝑝
∆𝑡
⟹
𝑑 Ԧ𝑝
𝑑𝑡
𝑊𝑡 = 𝑚𝑔
𝐴 𝑥 = ±𝐴 cos 𝜃 𝑅
𝐴 𝑦 = ±𝐴 sin 𝜃 𝑅
𝐹𝑓 = 𝜇𝑁
𝐹 = −𝑘𝑥 𝐹𝑔 =
𝐺𝑚1 𝑚2
𝑟2
𝐹𝑐 = 𝑚𝑎 𝑐 =
𝑚𝑣2
𝑅
= 𝑚𝑟𝜔2
𝐹𝑐 = 4𝜋2
𝑚𝑅𝑓2
𝐹𝑐 =
4𝜋2
𝑚𝑅
𝑇2
𝜏 = ±𝐹𝐿 = ±𝑟𝐹 sin 𝜃 𝑟⊥𝐹
𝑔 𝑝 =
𝐺𝑚 𝑝
(𝑅 𝑝 + ℎ )2
𝐸𝑃 = 𝑚𝑔ℎ
𝐸𝑀 = 𝐸𝑃 + 𝐸𝐾𝐸𝐾 =
1
2
𝑚𝑣2
Ԧ𝑝 = 𝑚 Ԧ𝑣 ∆ Ԧ𝑝 = 𝑚∆ Ԧ𝑣
𝜔 𝑓 = 𝜔𝑖 + 𝛼𝑡
ഥ𝜔 =
𝜔𝑖 + 𝜔 𝑓
2
𝜃 = ഥ𝜔𝑡
𝜃 = 𝜔𝑖 𝑡 +
1
2
𝛼𝑡2
𝜃 =
𝜔 𝑓
2
− 𝜔𝑖
2
2𝛼
𝑠 = 𝜃𝑅
𝑣 = 𝜔𝑅
𝑎 =∝ 𝑅
𝜏 = 𝐼𝛼
𝑊 = 𝐹𝑠 cos 𝜃 𝐹⊥𝑠
𝑊 = 𝜏𝜃
𝑊𝜏 = 𝜏𝜃 = ∆𝐾𝑟
𝑊𝐹 = ∆𝐾𝑡
𝑃 =
𝑊
𝑡
= 𝐹𝑣
𝑚1 𝑣1 + 𝑚2 𝑣2 = 𝑚1 + 𝑚2 Ԧ𝑣
Ԧ𝐼 = ∆ Ԧ𝑝
Ԧ𝐼 = Ԧ𝐹𝑡
ҧ𝑣 =
𝑑
𝑡
Ԧ𝑣 =
𝑑Ԧ𝑠
𝑑𝑡
𝑎 𝑐 =
𝑣2
𝑅
ഥ𝜔 =
𝜃
𝑡
Ԧ𝑎 =
𝑑 Ԧ𝑣
𝑑𝑡
Ԧ𝜏 =
∆𝐿
∆𝑡
⟹
𝑑𝐿
𝑑𝑡
𝐼 𝑎𝑟𝑜 = 𝑚𝑅2
𝐼 𝑑𝑖𝑠𝑐𝑜 =
1
2
𝑚𝑅2
𝐼𝑒𝑠𝑓𝑒𝑟𝑎 =
2
5
𝑚𝑅2
𝐼 𝑝𝑎𝑟𝑡𝑖𝑐𝑢𝑙𝑎 = 𝑚𝑅2
𝐼 =
𝑖=1
𝑛
𝑚𝑖 𝑟𝑖
2
⟹ න 𝑟2
𝑑𝑚
Ԧ𝐹 = 0
Ԧ𝜏 = 0
𝐹𝐴 = −𝐹𝑅
𝜏 𝐴 = −𝜏 𝑅
𝑇2
=
𝐺𝑚 𝑇
𝑅 𝑇 + ℎ 2
𝑃𝑒 =
1
2
𝑘𝑥2
𝑊 = න Ԧ𝐹 ∙ 𝑑Ԧ𝑠 ⟹ Ԧ𝐹 ∙ Ԧ𝑠
𝑃𝑔 = −
𝐺𝑚1 𝑚2
𝑟
∆𝑀 = 0
𝑊𝑛𝑐 = ∆𝑀
𝑃 = 𝜏𝜔
𝑊𝑛𝑒𝑡𝑜 = ∆𝐾
𝐾𝑟 =
1
2
𝐼𝜔2
𝑣𝑒 =
2𝐺𝑚 𝑝
𝑅 𝑝 + ℎ
𝐸𝑓𝑓 =
𝑊𝑜
𝑊𝑖
× 100% =
𝑃𝑜
𝑃𝑖
× 100% =
𝑉𝑀𝐴
𝑉𝑀𝐼
× 100%
∆ Ԧ𝑝 = 0
𝑚1 Ԧ𝑣1𝐴 + 𝑚2 Ԧ𝑣2𝐴 = 𝑚1 Ԧ𝑣1𝐷 + 𝑚2 Ԧ𝑣2𝐷
Ԧ𝜏 = 𝐼 Ԧ𝛼
Ԧ𝑣1𝐴 − Ԧ𝑣2𝐴 = Ԧ𝑣2𝐷 − Ԧ𝑣1𝐷
Ԧ𝐽 = Ԧ𝜏𝑡
𝐿 = Ԧ𝐼𝜔 = Ԧ𝑟 × Ԧ𝑝
Ԧ𝐽 = ∆𝐿 ∆𝐿 = 0
Ԧ𝐽 = Ԧ𝑟 × Ԧ𝐹 ⇒ 𝐹𝑟
𝑎 𝑐 = 4𝜋2
𝑓2
𝑅 𝑎 𝑐 = 𝜔2
𝑅
Cinemática Traslacional Cinemática Rotacional
Dinámica Traslacional Dinámica Espacial Dinámica Rotacional
Momento de Inercial
Cinemática
Proyecciones
Trabajo y Energía
Impulso y Momentum
PROF. PÉREZ SANABRIA 1FÓRMULAS DE FÍSICA
𝐴 = (𝐴 𝑥)2 + (𝐴 𝑦)2
𝜃 𝑅 = tan−1 Τ𝐴 𝑦 𝐴 𝑥
𝐹 = −𝑘𝑥
𝐹 = −𝑚𝑔 sin(𝜃)
𝐸𝑃 = 𝑚𝑔𝐿(1 − cos 𝜃)
𝑒 = 1 −
𝑏
𝑎
2
𝑟 𝑚𝑎𝑥 =
𝑏2
(𝑎 − 𝑑)
𝑟 𝑚𝑖𝑛 =
𝑏2
(𝑎 + 𝑑)
𝑇2
=
4𝜋2
𝐺𝑚
𝑟3
- 2. 𝑣 = 𝜆𝑓
𝑣 =
𝑇
𝜇
𝜇 =
𝑚
𝑙
𝑓𝑛 =
𝑛
2𝐿
𝑣
𝑦 𝑥, 𝑡 = 𝐴 sin 𝑘𝑥 ∓ 𝜔𝑡 + 𝛿
𝜔 = 2𝜋𝑓
𝑘 =
2𝜋
𝜆
𝑓𝑛 =
2𝑛 − 1
4𝐿
𝑣
𝑣 = 331 + 0.6𝑇
𝛽 = 10 log
𝐼
𝐼 𝑂
𝑣 =
𝛽
𝜌
𝑣 =
𝛾
𝜌
𝑣 =
𝜔
𝑘𝑓 = 𝑓′ 𝜈 ± 𝜈2
𝜈 ∓ 𝜈3
𝜌 =
𝑚
𝑉
𝑑 =
𝑊𝑡
𝑉
= 𝜌𝑔
𝐺ℇ =
𝜌𝑠𝑢𝑠𝑡
𝜌 𝐻2 𝑂
=
𝑑
𝑑 𝐻2 𝑂
𝐹
𝐴
= 𝛾
∆𝑙
𝑙0
𝐹
𝐴
= 𝛽
∆𝑉
𝑉0
𝐹
𝐴
= 𝑆𝜙 = 𝑆
𝑥
ℎ
℉ =
9
5
℃ + 32
∆𝑙
𝑙 𝑜
= 𝛼∆𝑇 = 𝑎∆𝑇
∆𝐴
𝐴 𝑜
= 𝛽∆𝑇 = 𝑏∆𝑇
∆𝑉
𝑉𝑜
= 𝛾∆𝑇 = 𝑐∆𝑇
𝐶 =
1
𝐵
𝑄 = 𝑚𝑐∆𝑇𝑄 = 𝑚𝐿
𝑃 =
𝐹⊥
𝐴
𝑃ℎ𝑒 = 𝜌𝑔ℎ
𝑃 =
𝑉𝑜𝑙
𝑡
= 𝐴𝑣
𝑃 +
1
2
𝜌𝑣2
+ 𝜌𝑔ℎ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡𝑒𝑃 = 𝑃𝑎𝑡𝑚 + 𝑃ℎ𝑒
PROF. PÉREZ SANABRIA 2
𝐴 𝑐𝑖𝑟𝑐𝑢𝑙𝑜 = 𝜋𝑟2
𝐴 𝑐𝑢𝑎𝑑𝑟𝑎𝑑𝑜 = 𝑙2
𝑉𝑐𝑖𝑙𝑖𝑛𝑑𝑟𝑜 = 𝜋𝑟2
ℎ
𝑉𝑒𝑠𝑓𝑒𝑟𝑎 =
4
3
𝜋𝑟3
𝑉𝑐𝑢𝑏𝑜 = 𝑙3
𝜃𝑖 = 𝜃 𝑅
sin 𝜃𝑖
sin 𝜃𝑟
=
𝑛 𝑟
𝑛𝑖
=
𝑣𝑖
𝑣𝑟
=
𝜆𝑖
𝜆 𝑟
1
𝑓
=
1
𝑑 𝑜
+
1
𝑑𝑖
1
𝑓
=
1
𝑓1
+
1
𝑓2
𝑚 = −
𝑑𝑖
𝑑 𝑜
= −
𝑡𝑖
𝑡 𝑜
sin 𝜃𝑖 =
𝑛 𝑅
𝑛𝑖
tan 𝜃 𝑅 =
𝑛 𝑅
𝑛𝑖
2𝑛𝑡 =
𝑚 + 1
2
𝜆
2𝑛𝑡 = 𝑚𝜆
𝑑 sin 𝜃 = 𝑚𝜆
𝑑 sin 𝜃 = 𝑚 −
1
2
𝜆
sin 𝜃 = 𝑚𝜆
sin 𝜃 =
𝑦
𝐿
𝜃 =
1.22𝜆
𝐷
Ondas y Vibraciones
Óptica
x 𝑡 = 𝐴 cos 𝜔𝑡 + 𝛿
𝑣 𝑡 = −𝐴𝜔 sin 𝜔𝑡 + 𝛿
𝑎 𝑡 = −𝐴𝜔2
cos 𝜔𝑡 + 𝛿
𝑃𝑢𝑙𝑠𝑎𝑐𝑖𝑜𝑛𝑒𝑠 = 𝑓1 − 𝑓2
𝑇 = 2𝜋
𝐼
𝑚𝑔𝑑
𝑇 =
𝑡
𝑛
=
1
𝑓
=
2𝜋
𝜔
𝑇 = 2𝜋
𝑙
𝑔
𝑇 = 2𝜋
𝑚
𝑘
Hidráulica
Propiedades de la materia
ME =
𝑆𝑡𝑟𝑒𝑠𝑠
𝑆𝑡𝑟𝑎𝑖𝑛
Calor
𝐾 = ℃ + 273
𝛾 = 2𝛼 β = 3𝛼
𝑄
𝑡
= −𝑘𝐴
∆𝑇
∆𝑥
𝑄 = 𝑊 + ∆𝑈
𝑊 = න 𝑝𝑑𝑉
𝐸𝑓𝑓 = 1 −
𝑇𝐶
𝑇 𝐻
× 100%
∆𝑆 =
∆𝑄
𝑇 ∆𝑆 ≥= 0
𝐹𝐵 = 𝑊𝑡 𝑟𝑒𝑎𝑙 − 𝑊𝑡 𝑎𝑝𝑙 = 𝜌𝑔𝑉𝑑𝑒𝑠𝑝𝑙
𝐹1
𝐴1
=
𝐹2
𝐴2
𝑃1 𝐴1 𝑣1 = 𝑃2 𝐴2 𝑣2
𝑣 = 2𝑔ℎ
𝑉𝑀𝐴 =
𝐹𝑜
𝐹𝑖
𝑉𝑀𝐼 =
𝐴 𝑜
𝐴𝑖
𝑃1 +
1
2
𝜌𝑣1
2
+ 𝜌𝑔ℎ1 = 𝑃2 +
1
2
𝜌𝑣2
2
+ 𝜌𝑔ℎ2
FÓRMULAS DE FÍSICA
- 3. 𝐾 =
𝑞
𝑞 − 𝑞𝑖
𝑅 𝑒𝑞 =
1
𝑛
𝑅𝑖
𝑅 𝑒𝑞 =
1
𝑛
1
𝑅𝑖
−1
𝑖 =
𝑞
𝑡
=
𝑉
𝑅
= 𝑛𝑞𝑣𝐴
𝑃 = 𝑖𝑉 = 𝑖2
𝑅 =
𝑉3
𝑅
ර 𝐵 ∙ 𝑑 Ԧ𝐴 = 0
𝐵 =
𝜇 𝑜 𝑖
4𝜋
න
𝑑𝑙 × Ƹ𝑟
𝑟2
ර 𝐵 ∙ 𝑑Ԧ𝑠 = 𝜇 𝑜 𝑖 𝑐 + 𝑖 𝑑
𝑗 =
𝑖
𝐴𝐵 =
𝜇 𝑜 𝑖
2𝜋𝑟
𝐵 =
𝜇 𝑜 𝑁𝑖
2𝑅
𝐵 = 𝜇 𝑜 𝑛𝑖
𝐵 =
𝜇 𝑜 𝑖𝜃
4𝜋𝑟
ර 𝐸 ∙ 𝑑Ԧ𝑠 = −𝑁
𝑑Φ 𝐵
𝑑𝑡
ℇ = −𝐿
𝑑𝑖
𝑑𝑡
ℇ = 𝐵𝑙𝑣
ℇ 𝑚 = 𝑁𝐵𝐴𝜔
ℇ = 𝑁𝐴
𝑑𝐵
𝑑𝑡
𝜔 =
𝑊
𝑉𝑜𝑙
𝜏 = 𝑅𝐶
𝜔 =
1
2
𝜀 𝑜 𝐸2
𝑖 𝑡 = 𝑖 𝑚 𝑒− ൗ𝑡
𝜏
𝑖 𝑡 = 𝑖 𝑚 1 − 𝑒− ൗ𝑡
𝜏
𝑊 =
1
2
𝑄𝑉 =
1
2
𝐶𝑉2
=
1
2
𝑄2
𝐶
𝑊 =
1
2
𝐿𝑖2
𝜏 =
𝐿
𝑅
𝜔 =
1
2
𝐵2
𝜇 𝑜
Φ = න 𝐵 ∙ 𝑑 Ԧ𝐴
Ԧ𝐹 = 𝑖Ԧ𝑙 × 𝐵
Ԧ𝐹 = 𝑞 Ԧ𝑣 × 𝐵
ℇ 𝑡 = ℇ 𝑚 𝑒− ൗ𝑡
𝜏
𝑞 𝑡 = 𝑞 𝑚 1 − 𝑒− ൗ𝑡
𝜏
∆𝑉 =
𝑊
𝑞
= − න 𝐸 ∙ 𝑑 Ԧ𝑠
𝑉 =
1
𝑛
𝑘𝑞𝑖
𝑟𝑖
𝑉 = 0
𝑖 = 0
ℇ = 𝑉𝑡 + 𝑖𝑟
𝑋 𝐿 = 2𝜋𝑓𝐿 = 𝜔𝐿
𝑋 𝐶 =
1
2𝜋𝑓𝐶
=
1
𝜔𝐶
𝑍 = 𝑅2 + 𝑋 𝐿 − 𝑋𝑐
2
𝑉𝑟𝑚𝑠 = 0.7072𝑉𝑚
𝑖 𝑟𝑚𝑠 = 0.7072𝑖 𝑚
𝑃 = 𝑖𝑉 cos 𝜙
𝑓𝑜 =
1
2𝜋 𝐿𝐶
𝑁1
𝑁2
=
𝑉1
𝑉2
=
𝑖2
𝑖1
=
𝑅1
𝑅2
E = ℎ𝑓
ϕ = ℎ𝑓𝑜
𝐸 = 𝐾 + ϕ
𝜃 =
𝜆
𝑑
PROF. PÉREZ SANABRIA 3
𝐸 =
𝑄
2𝜋𝜀 𝑜 𝑟𝑙
Ƹ𝑟
𝐶 =
𝐾𝜀 𝑜 𝐴
𝑑
Φ = ර 𝐸 ∙ 𝑑 Ԧ𝐴 =
σ 𝑞
𝜀 𝑜
=
𝑄
𝜀 𝑜
𝐶 =
𝑄
𝑉
K =
𝐶 𝑑
𝐶 𝑜
=
𝜀 𝑑
𝜀 𝑜
=
𝐸 𝑜
𝐸 𝑑
=
𝑉𝑜
𝑉𝑑
E =
𝑉
𝑑
Ԧ𝐹 =
𝑘𝑞1 𝑞2
𝑟2
Ƹ𝑟
𝐸 =
Ԧ𝐹
𝑞
𝐸 =
𝑘𝑞
𝑟2
Ƹ𝑟
𝐸 =
𝜎
𝐾𝜀 𝑜
Física Moderna
Electricidad y Magnetismo
FÓRMULAS DE FÍSICA
Φ = 𝐸 ∙ 𝐴 = 𝐸𝐴 cos 𝜃
PE =
𝑘𝑄𝑞
𝑟
V =
𝑘𝑄
𝑟
𝜂 =
1
2
𝜀𝐸2
𝑅 =
𝜌𝐿
𝐴
𝐹 = 𝑞𝑣𝐵 sin 𝜃
𝐹 = 𝑞 𝐸 + Ԧ𝑣 × 𝐵
𝐹 = 𝐼𝐿𝐵 sin 𝜃
𝜏 = 𝐼𝐴𝑛 × 𝐵𝐵 =
𝜇 𝑜 𝑛𝑖
ℎ
𝛾 =
1
1 − ൗ𝑣2
𝑐2
𝑢 =
𝑣 + 𝑢′
1 + ൗ𝑣𝑢′
𝑐2