Question

A wheel initially at rest is rotated with a uniform angular acceleration. The wheel rotates through an angle 1 in first on second and through an additional angle 2 in the next one second. The ratio 2 1

Answer 1

Answer: θ₂ : θ₁ = 3 : 1

Explanation:

The initial angular velocity of the wheel, ωo = 0 … [since it was at rest]

At first 1 sec, the wheel rotates through an angle = θ₁

And, in the next 1 second, the wheel rotates through an angle = θ₂

For t = 1 sec:

Using the eq. of angular motion, we get

θ₁ = ωot + ½ αt²

⇒ θ₁ = 0 + ½ α(1)²  

⇒ θ₁ = α/2 ….. (i)

For the next 1 second:

Here, t = 1 + 1 = 2 sec

Using the eq. of angular motion, we get

[θ₁ + θ₂] = ωot + ½ αt²

⇒ [θ₁+ θ₂]  = 0 + ½ α(2)²

⇒ [θ₁ + θ₂]  = 2α

⇒ θ₂ = 2α - α/2 ….. [substituting from (i)]

⇒ θ₂ = 3α/2 ….. (ii)

Thus, substituting the values from (i) & (ii), we get

The ratio of θ₂/ θ₁ as,

= [3α/2] / [α/2]

= 3