First slide

Dynamics of rotational motion about fixed axis

Question

A copper ball of mass m = 1 kg with a radius of r = 10 cm rotates with angular velocity $ω = 2 rad / s$ about an axis passing through its centre. The work should be performed to increase the angular velocity of rotation of the ball two fold is

Easy

A

$1.2 \times 10^{- 2} J$
B

$2.4 \times 10^{- 2} J$
C

$3.6 \times 10^{- 2} J$
D

$4.8 \times 10^{- 2} J$

Solution

K.E. = $\frac{1}{2} I ω^{2}$
If $ω$ is to be doubled
Therefore,W= $∆ K . E . = K . E ._{2} - K . E ._{1} = \frac{1}{2} I [{ω_{2}}^{2} - {ω_{1}}^{2}]$
$∆ K . E . = \frac{1}{2} \frac{2}{5} {mr}^{2} [{ω_{2}}^{2} - {ω^{2}}_{1}]$
= $\frac{2}{10} \times 1 [{(\frac{1}{10})}^{2}] [4^{2} - 2^{2}] = 2.4 \times 10^{- 2} J$

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