Question

A flywheel of moment of inertia $9.8kg{m}^2$ fluctuates by 30 rpm for a fluctuation in energy of 1936 joules. The mean speed of the flywheel is (in rpm)

• A. 600
• B. 900
• C. 968
• D. 29470

Answer 1

The correct option is A 600

Given data:
$I=9.8kg{m}^2$
$N_1-N_2=30\text{rpm}$
$\Delta E=1936J$
$N_{mean}=?$

$C_s=\frac{\frac{N_1-N_2}{N_1+N_2}}{2}=\frac{N_1-N_2}{N_{mean}}=\frac{30}{N_{mean}}$

$\Delta E=I{\omega }_{mean}^2{C}_s$

${\omega }_{mean}=\frac{2\pi N_{mean}}{60}$

$\Delta E=I{\left\{\frac{2\pi N_{mean}}{60}\right\}}^2{C}_s$

$\Delta E=I{\{\frac{2\pi }{60}.N_{mean}\}}^2\frac{30}{N_{mean}}$

$\Delta E{\left(\frac{2\pi }{60}\right)}^2\times 30\times N_{means}$

$N_{mean}=\frac{\Delta E}{I{\left(\frac{2\pi }{60}\right)}^2\times 30}=\frac{1936}{9.8\times {\left\{\frac{2\pi }{60}\right\}}^2}\times 30$

$=600.48$ rpm