Question

The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.
The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. For fluctuation in the speed to be within $\pm$2% of the average speed the mass moment of inertia of the flywheel is kgm${}^2$

• A. 3.58

Answer 1

The correct option is A 3.58
Given ($T-\theta$) diagram :
$N=1000\text{rpm}$

$\omega =\frac{2\pi \times 1000}{60}=104.7195\text{rad/s}$

$\Delta E_{max}=(\pi -\frac{\pi }{2}).(3000-2000)$

$=(\frac{\pi }{2}\times 1000)\text{J}$

$C_s=\pm 2\%=4\%=0.04$

$\Delta E_{max}=I.{\omega }^2.C_s$

$\frac{\pi }{2}\times 1000=I\times (104.7195{)}^2\times 0.04$

$I=\frac{1570.795}{(104.7195{)}^2\times 0.04}$

$=3.58kg-m^2$