Kinematics of rotation

With the axis fixed, a single angle θ describes the whole body (one degree of freedom). It is read for any one particle, from a fixed reference line in that particle's plane of motion.

θ, ω = dθ/dt and α = dω/dt correspond to x, v and a in linear motion.

For constant α: ω = ω₀ + αt, θ = θ₀ + ω₀t + ½αt², and ω² = ω₀² + 2α(θ − θ₀), where θ₀ and ω₀ are the values at t = 0.

ω = ω₀ + αt follows by integrating dω/dt = α with ω = ω₀ at t = 0; integrating once more gives the θ equation.

Convert rpm to rad/s by multiplying by 2π/60. 1200 rpm = 40π rad/s and 3120 rpm = 104π rad/s.

A motor wheel going from 1200 rpm to 3120 rpm in 16 s at constant α: α = (104π − 40π)/16 = 4π rad/s². It turns through θ = 40π × 16 + ½ × 4π × 16² = 1152π rad, that is 576 revolutions.