First slide

Kinematics of rotational motion about fixed axis

Question

A solid body rotates with deceleration about a stationary axis with an angular deceleration $|α| = k \sqrt{ω}$ ; where k is a constant and $ω$ is the angular velocity of the body. If the initial angular velocity is $ω_{0}$ , then time taken by the body to come to rest—

Difficult

A

$\frac{2 \sqrt{ω_{o}}}{k}$
B

$\frac{4 \sqrt{ω_{o}}}{k}$
C

$\frac{\sqrt{ω_{o}}}{k}$
D

$\frac{\sqrt{ω_{o}}}{2 k}$

Solution

$- α = k \sqrt{w}$
$- \frac{d w}{d t} = k \sqrt{w}$
$- \int_{ω_{o}}^{o} \frac{d w}{\sqrt{w}} = k d t$
$\frac{ω_{0}^{(- \frac{1}{2} + 1)}}{- \frac{1}{2} + 1} = k t$
$2 \sqrt{ω_{o}} = k t$
$t = \frac{2 \sqrt{ω_{o}}}{K}$

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