calculate the magnitude of the angular deceleration of the wheel, in rad s-2

Question

As the brakes are applied to a bicycle wheel, the angular velocity of the wheel changes from 63 rad s^-1 to 34 rad s^-1.If the wheel turns through exactly 16 revolutions whilst the brakes are being applied

Answer 1

We use formula: ω² - ω₀² = 2φε, where ω = 34 rad/s, ω₀ = 63 rad/s and φ = 2π·16 = 32π rad;

So angular accelaration ε = (ω² - ω₀²)/(2φ) = (34² - 63²)/64π) = - 14 rad/s²