# Question #92227

Mar 21, 2017

The torque is $= 18816 N m$

#### Explanation:

The torque is the rate of change of angular momentum

$\tau = \frac{\mathrm{dL}}{\mathrm{dt}} = \frac{d \left(I \omega\right)}{\mathrm{dt}} = I \frac{\mathrm{do} m e g a}{\mathrm{dt}}$

The moment of inertia of a circular disc is

$I = \frac{1}{2} \cdot m {r}^{2}$

$= \frac{1}{2} \cdot 2800 \cdot {28}^{2} = 1097600 k g {m}^{2}$

The rate of change of angular velocity is

$\frac{\mathrm{do} m e g a}{\mathrm{dt}} = \frac{0.24}{14} = 0.0171 r a {\mathrm{ds}}^{-} 2$

So the torque is $\tau = 1097600 \cdot \left(0.0171\right) N m = 18816 N m$