Answer to Question #277536 in Physics for Dhea

Question

A propeller with three blades of mass 12 kg each, length of 1.25 m each are 120 degrees relative to each other. If a torque 3000 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 2000 rad/s starting from rest?

Answer 1

The moment of inertia:

$$I=3·\frac13mr^2=18.75\text{ kg}·\text{m}^2.$$

How long it will take to reach an angular velocity of 2000 rad/s starting from rest. First, find the acceleration:

$$\alpha=\tau/I=3000/18.75=160\text{ rad/s}^2.$$

Second, find the time:

$$t=\frac{\omega}{\alpha}=12.5\text { s}.$$