Rotational dynamics · Grade 11
Spinning objects obey rules that mirror straight-line motion. Torque plays the part of force, moment of inertia plays the part of mass, and angular velocity plays the part of velocity. These ideas explain why skaters spin faster with their arms pulled in and how flywheels store energy.
Key facts
- Torque τ = rF (force × perpendicular distance from the axis).
- Moment of inertia I = Σmr²: point mass mr², solid disc ½MR², hoop MR².
- τ = Iα (the rotational version of F = ma).
- Rotational kinetic energy = ½Iω²; angular momentum L = Iω.
- With no external torque, angular momentum is conserved: I₁ω₁ = I₂ω₂.
- Rotational kinematics: ω = ω₀ + αt, θ = ω₀t + ½αt²; work W = τθ, power P = τω.