Answer to Question #274923 in Physics for Dhea

Question

A propeller with three blades of mass 12 kg each , length of 1.25m each are 120 degrees relative to each other. If a torque N.m acts on this, what is the moment of inertia of the propeller? How long will it take to reach an angular velocity of 2000rad/s starting from rest?

Answer 1

The moment of inertia of the propeller:

$$I=mL^2.$$

Upon the torque $\tau$, the angular acceleration is

$$\alpha=\tau/I=\tau/(mL^2)=\tau/18.75\text{ rad/s}^2.$$

The time it takes to reach 2000 rad/s stating from rest:

$$t=\frac{\omega}{\alpha}=\frac{\omega I}{\tau}=\frac{\omega mL^2}{\tau}=\frac{37500}\tau\text{ s}.$$