Acar wheel turning at 0.5 rad/s is brought to rest by the brakes in exactly two revolutions. what is the angular acceleration of the wheel?

w₀ = initial angular velocity of the car wheel = 0.5 rad/s

w = final angular velocity of the car wheel = 0 rad/s

n = number of revolutions revolved by wheel before coming to rest = 2

θ = angular displacement = 2nπ = 2 x 2 x 3.14 = 12.56 rad

α = angular acceleration of the wheel = ?

using the equation

w² = w₀² + 2 αθ

0² = 0.5² + 2 (12.56) α

α = - 9.95 x 10⁻³ rad/s²