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 $5rev/s$ to $10rev/s$ is approximately

• A. $1.5\times {10}^{2}J$
• B. $3.0\times {10}^{2}J$
• C. $1.5\times {10}^{3}J$
• D. $3.0\times {10}^{3}J$

Answer 1

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

$W=K_f-K_i$
$W=\frac{1}{2}I({\omega }_f^2-{\omega }_i^2)=\frac{1}{2}\left(\frac{1}{2}M{R}^2\right)({\omega }_f^2-{\omega }_i^2)$
$=\frac{1}{4}\times 2\times 1^2\left[\right(2\pi \times 10{)}^2-(2\pi \times 5{)}^2]=1.5\times {10}^{3}J$