Physics 11 Final

Velocity

𝑣(𝑡) = 𝑑𝑥(𝑡)/𝑑𝑡

Acceleration

𝑎(𝑡) = 𝑑𝑣(𝑡)/𝑑𝑡

Average Velocity

𝑣𝑎𝑣𝑔 = Δ𝑥/Δ𝑡

Constant Acceleration (Velocity)

𝑣(𝑡) = 𝑣(0) + 𝑎𝑡

Constant Acceleration (Position)

𝑥(𝑡) = 𝑥(0) + 𝑣(0)𝑡 + (1/2)𝑎𝑡²

Centripetal Acceleration

𝑎𝑐 = 𝑣²/𝑟

Newton's Second Law

𝐹𝑛𝑒𝑡 = 𝑚𝑎

Gravity (Near Earth)

𝐹𝑔 = 𝑚𝑔

Gravity (Universal)

𝐹𝑔 = (𝐺𝑀₁𝑀₂)/𝑟²

Friction (Static)

𝐹𝑓 ≤ μₛ𝑁

Friction (Kinetic)

𝐹𝑓 = μₖ𝑁

Spring Force

𝐹𝑠𝑝𝑟𝑖𝑛𝑔 = -𝑘𝑥

Work-Energy Theorem

𝑊 = Δ𝐾.𝐸.

Kinetic Energy

𝐾.𝐸. = (1/2)𝑚𝑣²

Work (Dot Product)

𝑊 = 𝐹⋅Δ𝑟 cos(𝜃)

Potential Energy (Gravity)

𝑈𝑔 = 𝑚𝑔ℎ

Potential Energy (Spring)

𝑈𝑠 = (1/2)𝑘𝑥²

Conservation of Mechanical Energy

𝐸 = 𝐾.𝐸. + 𝑃.𝐸.

Momentum

𝑝 = 𝑚𝑣

Impulse

𝐽 = Δ𝑝 = 𝐹Δ𝑡

Impulse (Integral)

𝐽 = ∫𝐹 𝑑𝑡

Conservation of Momentum

𝑝𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝑝𝑓𝑖𝑛𝑎𝑙

Angular Momentum (Point Mass)

𝐿 = 𝑟 × 𝑝

Angular Position

𝜃 = 𝑠/𝑟

Angular Velocity

𝜔 = 𝑑𝜃/𝑑𝑡

Angular Acceleration

𝛼 = 𝑑𝜔/𝑑𝑡

Moment of Inertia (Point Mass)

𝐼 = ∑𝑚𝑖𝑟𝑖²

Rotational Kinetic Energy

𝐾.𝐸. = (1/2)𝐼𝜔²

Torque

𝜏 = 𝑟𝐹 sin(𝜃)

Newton's Second Law (Rotation)

𝜏 = 𝐼𝛼

Angular Momentum

𝐿 = 𝐼𝜔

Conservation of Angular Momentum

𝐿𝑖𝑛𝑖𝑡𝑖𝑎𝑙 = 𝐿𝑓𝑖𝑛𝑎𝑙