Question

A wheel is Subjected to uniform angular acceleration about its axis. Initially. its angular velocity is zero. In the first 2 s, it rotates through an angle θ₁, in the next 2 s, it rotates through an angle θ₂. The ratio of `theta_2/theta_1` is ______.

पर्याय

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Answer 1

A wheel is Subjected to uniform angular acceleration about its axis. Initially. its angular velocity is zero. In the first 2 s, it rotates through an angle θ₁, in the next 2 s, it rotates through an angle θ₂. The ratio of `theta_2/theta_1` is 3.

Explanation:

θ = ωt `1/2` αt²

Where θ is the angle, ω is the angular velocity, t is the time and α is the angular acceleration.

Consider the first situation

θ₁ = `omega_0"t"+1/2alpha"t"^2`

⇒ θ₁ = `(0)"t"+1/2alpha(2)^2`

∴ θ₁ = 2α

Let the angular velocity changes from ω₀ to ω′

Then the final angular velocity is given as follows

ω′ = ω₀ + αt

⇒ ω′ = 0 + α(2)

∴ ω′ = 2α

Consider the second situation

θ₂ = `omega"'""t"+1/2alpha"t"^2`

⇒ θ₂ = `(2alpha)2+1/2alpha(2)^2`

∴ θ₂ = 6α

Now we will compute the ratio of the angles

`theta_2/theta_1=(6alpha)/(2alpha)`

⇒ `theta_2/theta_1=6/2`

∴ `theta_2/theta_1` = 3