Rotational dynamics

CALIBRANT
Physics Formula Sheet 12th STD


ROTATIONAL DYNAMICS

1. In U.C.M angular velocity

v
i. ω = 𝑖𝑖𝑖. 𝜔 = 2𝜋𝑛
r

𝜃 2𝜋
𝑖𝑖. 𝜔 = 𝑖𝑣. 𝜔 =
𝑡 𝑇




2. Angular Displacement

𝑖. 𝜃 = 𝜔𝑡 𝑖𝑖𝑖 . 𝜃 = 2𝜋𝑛𝑡
2𝜋
𝑖𝑖. 𝜃 =
𝑇



3. Angular Acceleration

𝜔2 − 𝜔1
𝑖. 𝛼 =
𝑡


2𝜋
𝑖𝑖. 𝛼 = (𝑛2 − 𝑛1)
𝑡



4. Linear Velocity

𝑖. 𝑣 = 𝑟𝜔


𝑖𝑖. 𝛼 = 2𝜋𝑛𝑟



5. Centripetal Acceleration or Radial Acceleration


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, CALIBRANT
Physics Formula Sheet 12th STD


ROTATIONAL DYNAMICS
𝑣2
𝑎= = 𝜔 2𝑟
𝑟



6. Tangential Acceleration

𝑎𝑇 = 𝛼⃗ × 𝑟⃗
⃑⃑⃑⃑



7. Centripetal Force

𝑚𝑣2 4𝜋 2𝑚𝑟
𝑖. 𝐹𝐶𝑃 = 𝑖𝑣. 𝐹𝐶𝑃 =
𝑇2
𝑟



𝑖𝑖. 𝐹𝐶𝑃 = 𝑚𝑟𝜔 2 𝑣. 𝐹𝐶𝑃 = 𝜇𝑚𝑔 = 𝑚𝜔 2𝑟



𝑖𝑖𝑖 . 𝐹𝐶𝑃 = 4 𝜋 2 𝑚𝑟𝑛2



8. Centrifugal Force

𝐹𝐶𝐹 = −𝐹𝐶𝑃



9. Inclination of Banked Road

𝑣2
𝜃 = 𝑡𝑎𝑛−1 ( )
𝑟𝑔




10. On unbanked Road

𝑖. 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑣𝑒ℎ𝑖𝑐𝑙𝑒 𝑡𝑜 𝑎𝑣𝑜𝑖𝑑 𝑠𝑘𝑖𝑑𝑑𝑖𝑛𝑔 𝑜𝑛 𝑎 𝑐𝑢𝑟𝑣𝑒 𝑢𝑛𝑏𝑎𝑛𝑘𝑒𝑑 𝑟𝑜𝑎𝑑:𝑣𝑚𝑎𝑥 = √𝜇𝑟𝑔


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