A 350-kg disk (with uniform density) is shown below. Its rotation axis is through its center. If the disk is initially at rest, how long does it take to reach an angular velocity of 25 rad/s? 4 20 N 18 N 0.25 m 0.75 m 1.0 m 0.5 m 16 N D. Е. А. 152.6 s 163.5 s В. 164.5 s 141.1 s С. 120.0 s F. 137.0 s

Mass of the disc $\left(M\right)=350 \text{kg}$

Final angular velocity of the disc $\left(\omega \right)=25 \text{rad/s}$

Radius of the disc $\left(R\right)=1 \text{m}$

The moment of inertia of this uniform disc is given by;

$I=\frac{1}{2}M{R}^2$

Substituting the values;

$I=\frac{1}{2}\times 350\times {\left(1\right)}^2$

$\therefore I=175 {\text{kg m}}^2$

According to the diagram, there are three different forces acting on the disc. Hence, the net torque on this disc at its center will be;

$\tau =(20\times 0.25)+(18\times 1)+(16\times 0.5)$

$\therefore \tau =31 {\text{N m}}^2$