Answer to Question #158107 in Mechanics | Relativity for aleyna

Question

A flywheel of rotational inertia I = 53kg⋅m2 rotates with angular speed 4.0 rad/s. A tangential force of 6.5 N is applied at a distance of 0.36 m from the center in such a way that the angular speed decreases. How long will it take the wheel to stop?

Result: 100 s

Answer 1

Let's find the torque that acts on the flywheel to stop it:

$$\tau=Fr=-6.5\ N\cdot0.36\ m=-2.34\ N\cdot m.$$

From the other hand, torque can be written as follows:

$$\tau=\alpha I.$$

Then, we can find the angular decceleration of the flywheel:

$$\alpha=\dfrac{\tau}{I}=\dfrac{-2.34\ N\cdot m}{53\ kg\cdot m^2}=-0.04\ \dfrac{rad}{s^2}.$$

Finally, we can find the time that the flywheel takes to stop:

$$\alpha=\dfrac{\omega-\omega_0}{t},$$ $$t=\dfrac{0-4\ \dfrac{rad}{s}}{-0.04\ \dfrac{rad}{s^2}}=100\ s.$$