Posted by Zach on .
A 60-cm-long, 500 g bar rotates in a horizontal plane on an axle that passes through the center of the bar. Compressed air is fed in through the axle, passes through a small hole down the length of the bar, and escapes as air jets from holes at the ends of the bar. The jets are perpendicular to the bar's axis. Starting from rest, the bar spins up to an angular velocity of 150 rpm at the end of 10 s. How much force does each jet of escaping air exert on the bar? If the axle is moved to one end of the bar while the air jets are unchanged, what will be the bar's angular velocity at the end of 10 seconds?
The part about moving the axle is rather confusing. I assume they mean doing the experiment over again with the axis at the end of the bar. The angular speed at the end of the 10 s will be less than for the first case (also after 10 seconds) for two reasons:
(1) Only one jet produces a torque about the axle, and
2) The moment of inertia of the bar is greater with the axle at the end.
To get the jet force, use this relation for the axle-in-the-middle case:
Torque = 2*(force)*(lever arm)
= (Moment of inertia*(angular acceleration rate)