Answer to Question #174055 in Physics for Andu

Question

12. A flywheel has an inertia moment of 3.5 kgm². Find the moment of force to be exerted on it, so that in 10 seconds it reaches the frequency 360 rpm, uniformly accelerated.

Answer 1

Let's first find the angular acceleration of the flywheel:

$$\alpha=\dfrac{\omega-\omega_0}{t},$$ $$\alpha=\dfrac{360\ \dfrac{rev}{min}\cdot\dfrac{1\ min}{60\ s}\cdot\dfrac{2\pi\ rad}{1\ rev}}{10\ s}=3.77\ \dfrac{rad}{s^2}.$$

Then, we can find the moment of force to be exerted on the flywheel:

$$\tau=I\alpha=3.5\ kg\cdot m^2\cdot3.77\ \dfrac{rad}{s^2}=13.2\ N\cdot m.$$