First slide

Dynamics of rotational motion about fixed axis

Question

If 484 J of energy is spent in increasing the speed of a wheel from 60 rpm to 360 rpm, the M.I. of the wheel is

Moderate

A

1.6 kg m²
B

0.3 kg m²
C

0.7 kg m²
D

1.2 kg m²

Solution

$\large {\omega _1} = 60 \times \frac{{2\pi }}{{60}} = 2\pi \;rad/s$
$\large {\omega _2} = 360 \times \frac{{2\pi }}{{60}} = 12\pi \;rad/s$
$\large KE = \frac{1}{2}I\left( {\omega _2^2 - \omega _1^2} \right)$
$\large 484 = \frac{1}{2}I\left( {{{\left( {12\pi } \right)}^2} - {{\left( {2\pi } \right)}^2}} \right)\left( {{\pi ^2} = 10} \right)$
$\large 484 = \frac{1}{2}I\left( {1440 - 40} \right)$
$\large {\rm{I = 0}}{\rm{.7}}\;{\rm{kg}}{{\rm{m}}^{\rm{2}}}{\rm{ }}$

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