Question

The rim of a flywheel has mass of $10\text{kg}$ and having radius ${}^{\prime }{r}^{\prime }$. A force of $500\text{N}$ is acting tangentially which produces angular acceleration of $3{\text{rad/s}}^2$. Calculate the radius of the flywheel.

• A. $4\text{m}$
• B. $8.83\text{m}$
• C. $16.67\text{m}$
• D. None of these

Answer 1

The correct option is C $16.67\text{m}$


$\therefore$ Torque produced, $\tau =r\times F$
$\Rightarrow \tau =r\times 500\text{Nm}$
Also, we know that
$\tau =I\alpha$
$I$ (for rim) $=M{r}^2=10r^2$
$\Rightarrow r\times 500=10r^2\times 3$
$\Rightarrow r=\frac{500}{30}$
Radius $\Rightarrow r=16.67\text{m}$

Alternate:
Since the force is acting tangentially, which is given by
$F_t=m{a}_t=mr\alpha$
$\Rightarrow 500=10\times r\times 3\Rightarrow r=\frac{500}{30}=16.67\text{m}$