Question

A fly wheel is in the form of a uniform circular disc of radius $1\text{m}$ and mass $2\text{kg}$. The work which must be done on it to increase its frequency of rotation from $5\text{rev/s}$ to $10\text{rev/s}$ is approximately

• A. $1.5\times {10}^2\text{J}$
• B. $3\times {10}^2\text{J}$
• C. $1.5\times {10}^3\text{J}$
• D. $3\times {10}^3\text{J}$

Answer 1

The correct option is C $1.5\times {10}^3\text{J}$

W = change in rotational kinetic energy $=\frac{1}{2}I({\omega }_f^2-{\omega }_i^2)$
$=\frac{1}{2}\left(\frac{1}{2}m{R}^2\right)\left[\right(2\pi f_f{)}^2-\left(2\pi f_i{)}^2\right]$
$=\frac{1}{4}\times 2\times (1{)}^2\times 4\times {\pi }^2(100-25)$
$=1.48\times {10}^{3}J\approx 1.5\times {10}^3\text{J}$