A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

Solution

Physics sir · 3 steps

Get the angular acceleration from the first second, then subtract: total after 2 s minus the first 5 rad.

1. Find the acceleration. Starting from rest, θ = 1/2α t². In the first second, 5 = 1/2α (1)², so α = 10 rad s⁻².
2. Angle after two seconds. θ₂ = 1/2 × 10 × (2)² = 20 rad. This is the total angle turned from t = 0 to t = 2 s.

   θ_(2nd second) = θ₂ - θ₁ = 20 - 5 = 15 rad

3. So. The flywheel turns through 15 rad in the next second, which is option (b). This matches the 1 : 3 : 5 pattern for equal seconds from rest: 5 × 3 = 15.

The idea to keep. Starting from rest with uniform acceleration, the angles turned in successive equal seconds go as 1 : 3 : 5 : …, just like distances in linear motion.

Answer from the NTA final answer key. Solution by PrepWiser.