Question

An electric motor exerts a constant torque 10 N-m on a grind stone mounted on a shaft. MOI of the grind stone about the shaft is 2kg $m^{-2}$. If the system starts from rest, find the work done in 8s.

• A. $1600J$
• B. $1200J$
• C. $800J$
• D. $600J$

Answer 1

The correct option is A $1600J$

$a=\frac{\tau }{I}=\frac{10}{2}=5rad/s^2$.
$\omega ={\omega }_0+at=5\left(8\right)=40rad{s}^{-1}$.
$W=\Delta KE=\frac{1}{2}I{\omega }^2-0=\frac{1}{2}\times 2\times (40{)}^2=1600J$