A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle ₁ and in the next 2 s it rotates through an angle ₂ . The ratio ₂ ₁ is _______.

Step-by-step solution

Using the equation of rotational kinematics = ₀ t + 1 2 t^2 . Since the wheel is initially at rest, ₀ = 0 . Angle rotated in the first 2 s : ₁ = 1 2 (2)^2 = 2 Angle rotated in the first 4 s : _ total = 1 2 (4)^2 = 8 Angle rotated in the next 2 s : ₂ = _ total - ₁ = 8 - 2 = 6 The ratio is: ₂ ₁ = 6 2 = 3 Answer: 3