Question

A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ_1, in first two seconds. In the next two seconds, it rotates through an angle θ₂. The ratio θ₁/θ₂ is ____________.

Options

• `1/3`

• `1/4`

• `1/2`

• `1/6`

Answer 1

A wheel is subjected to uniform angular acceleration about its axis. The wheel is starting from rest and it rotates through an angle θ_1, in first two seconds. In the next two seconds, it rotates through an angle θ₂. The ratio θ₁/θ₂ is  `1/3`.

Explanation:

ln the first 2s the angular displacement of the body

= `theta = omega _0t + 1/2  alphat^2`

⇒ `theta_1 = 0 + 1/2 alpha × 4 = 2alpha`

After a time interval of 4s, the angular displacement of the body = `theta = omega_0t + 1/2 alphat^2`

⇒ `theta = 0 + 1/2alpha × 16 = 8alpha`

To find, the angular displacement in the next 2s, i.e. `theta_2 = theta - theta_1 = 6alpha`

Ratio `theta_1/theta_2 = (2alpha)/(6alpha) = 1/3`