A wheel starts from rest and rotates with uniform angular acceleration about its fixed axis. During the first 2 s it turns through an angle θ₁. During the next 2 s, from t = 2 s to t = 4 s, it turns through an angle θ₂. What is the ratio θ₂ / θ₁?
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Question

A wheel starts from rest and rotates with uniform angular acceleration about its fixed axis. During the first 2 s it turns through an angle θ₁. During the next 2 s, from t = 2 s to t = 4 s, it turns through an angle θ₂. What is the ratio θ₂ / θ₁?

Options

G1 Physics · Accepted Answer

For uniform angular acceleration α and zero initial angular speed, θ = (1 ÷ 2)αt². During the first 2 s: θ₁ = (1 ÷ 2)α(2)² = 2α. The total angle turned in the first 4 s is θ(4) = (1 ÷ 2)α(4)² = 8α. Therefore the angle turned during the next 2 s is θ₂ = θ(4)-θ₁ = 8α-2α = 6α. Hence, θ₂ ÷ θ₁ = 6α ÷ 2α = 3. Correct option: B.