@electroniceducation: This image is a Physics Mechanics Formula Sheet. It contains important formulas related to rotation, torque, angular momentum, and energy. 1. Moment of Inertia (I) Moment of inertia measures how difficult it is to rotate an object. Ring: I = MR² Solid Disc: I = ½MR² Solid Cylinder: I = ½MR² Rod (about center): I = ¹⁄₁₂ML² Rod (about end): I = ⅓ML² Point Mass: I = mr² Where: M = mass R = radius L = length r = distance from axis 2. Parallel-Axis Theorem Used when the rotation axis is not through the center of mass. I = Icm + Md² Where: Icm = moment of inertia about center of mass d = distance between axes 3. Torque and Rotational Equilibrium Torque is the turning effect of a force. τ = r × F Magnitude: τ = rF sinθ For equilibrium: Στ = 0 Static equilibrium: ΣF = 0 and Στ = 0 4. Angular Momentum Rotational version of momentum. For a particle: L = r × p Magnitude: L = rp sinθ For a rotating rigid body: L = Iω Conservation: Li = Lf 5. Rotational Kinetic Energy Rotating object: K = ½Iω² Rolling object: K = ½Iω² + ½mv² Translational motion only: K = ½mv² 6. Work, Power and Conservation Work done by torque: W = τΔθ Work-Energy Theorem: Wnet = ΔK = Kf − Ki Power: P = dW/dt = τω Conservation of Mechanical Energy: Ki + Ui = Kf + Uf Symbols I = Moment of Inertia M, m = Mass R = Radius L = Length r = Distance from axis F = Force τ = Torque ω = Angular speed K = Kinetic Energy θ = Angle P = Power This sheet is a quick reference for rotational mechanics in physics.
