Question: A wheel of radius 0.5 meters starts from rest and takes 5 seconds to reach an angular velocity of 10 radians per second. Assuming constant angular acceleration, determine the magnitude of the angular acceleration of the wheel.

Answer: Given: Initial angular velocity, ω₁ = 0 radians/second (as it starts from rest) Final angular velocity, ω₂ = 10 radians/second Time, t = 5 seconds Radius, r = 0.5 meters We know the formula for angular acceleration (α) in rotations with constant angular acceleration:

α = (ω₂ - ω₁) / t

Substituting the given values:

α = (10 - 0) / 5 α = 2 radians/second²

Hence, the magnitude of the angular acceleration of the wheel is 2 radians/second².