A wheel initially at rest is subjected to a uniform angular acceleration about its axis

Question

A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $θ_{1}$ and in the next 2 s it rotates through an angle $θ_{2}$ . The ratio $\frac{θ_{2}}{θ_{1}}$ is ______. [2026]

Smart Achievers · Accepted Answer

(2)

$Let α be angular acceleration$

$In first 2 sec, θ_{1} = \frac{1}{2} α {(2)}^{2} = 2 α$

$θ' = \frac{1}{2} (α) {(4)}^{2} = 8 α$

$θ_{2} = θ' - θ_{1} = 8 α - 2 α = 6 α$

$\Rightarrow \frac{θ_{2}}{θ_{1}} = \frac{6 α}{2 α} = 3$

Solution

Q.
A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle $θ_{1}$ and in the next 2 s it rotates through an angle $θ_{2}$ . The ratio $\frac{θ_{2}}{θ_{1}}$ is ______. [2026]

1 $6$

2 $3$

3 $4$

4 $\frac{1}{3}$

Ans.
(2)

$Let α be angular acceleration$

$In first 2 sec, θ_{1} = \frac{1}{2} α {(2)}^{2} = 2 α$

$θ' = \frac{1}{2} (α) {(4)}^{2} = 8 α$

$θ_{2} = θ' - θ_{1} = 8 α - 2 α = 6 α$

$\Rightarrow \frac{θ_{2}}{θ_{1}} = \frac{6 α}{2 α} = 3$

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