First slide

Angular velocity, Angular acceleration

Question

A car wheel is rotated to uniform angular acceleration about its axis. Initially, its angular velocity is zero. It rotates through an angle $θ$ ₁ in the first 2 s. In the next 2 s, it rotates through an additional angle $θ$ ₂ , the ratio of $\frac{θ_{2}}{θ_{1}}$ is

Moderate

A

1
B

2
C

3
D

4

Solution

$α = constant$
$∴ θ = \frac{1}{2} α t^{2}$
$∵ θ \propto t^{2}$
or $\frac{θ_{2} + θ_{1}}{θ_{1}} = {(\frac{2 + 2}{2})}^{2} = 4 or \frac{θ_{2}}{θ_{1}} = 3$

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