Rotational motion
Rotation has its own position, velocity, acceleration, inertia, force effect and momentum. Each has a direct connection to linear motion.
1. Angular description
Angular displacement θ is measured in radians, with one revolution equal to 2π rad. Angular velocity is ω = Δθ/Δt and angular acceleration is α = Δω/Δt. For a point at radius r, arc length s = rθ, tangential speed v = rω, and tangential acceleration at = rα. Points on one rigid body share ω but have different tangential speeds when their radii differ.
2. Torque and rotational inertia
A force turns most effectively when perpendicular to the radius: τ = rF sin θ. The rotational form of Newton's second law is Στ = Iα. Moment of inertia I measures resistance to angular acceleration and depends on how mass is distributed relative to the axis. For point masses, I = Σmr²; moving the same mass outward increases I strongly because radius is squared.