First slide

Dynamics of rotational motion about fixed axis

Question

A flywheel is in the form of a uniform circular disc of radius 1 m and mass 2 kg. The work which must be done on it to increase its frequency of rotation from 5 rps to 10 rps is approximately

Moderate

A

1.5 X 10² J
B

3.0 X 10² J
C

1.5 x 10³ J
D

3.0 x 10³ J

Solution

W = Change in rotational kinetic energy $= \frac{1}{2} I (ω_{f}^{2} - ω_{i}^{2})$
$= \frac{1}{2} (\frac{1}{2} m R^{2}) [{(2 π f_{f})}^{2} - {(2 π f_{i})}^{2}]$
$= (\frac{1}{4} m R^{2}) [4 π^{2} (f_{f}^{2} - f_{i}^{2})]$
$= \frac{1}{4} \times 2 \times (1)^{2} \times 4 \times π^{2} (100 - 25)$
$= 1.48 \times 10^{3} J \approx 1.5 \times 10^{3} J$

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