A 60cm long, 500g bar rotates in a horizontal plane on an axle that passes throu

Question

A 60cm long, 500g 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 lenght of the bar, and escapes as air jets from holes at the ends of the bar. The jests 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 10s.

a) How much force does each jet of escaping air exert on the bar?

b) 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?

Explanation / Answer

Moment about center of the bar:
M = I ang acel = F L
Then, the force F is:
F = I ang acel / L

I = moment of inertia = 1/12 m L^2
ang acel = w / t = (2pi/60 * n) / t = pi n / 30 t
Replacing
F = (1/12 m L^2) * ( pi n /30 t) / L
F = pi m L n / 360 t
F = 3.1416 0.5kg 0.6m 150rpm / 360 10s
F = .04N.................Answer for (a)

Bar rotates around one of its ends:
I = 1/3 m L^2

M = F L = I pi n / 30 t
F L = 1/3 m L^2 pi n / 30 t
F = m L pi n / 90 t
n = 90 t F / m L pi
n = 90 10s .04N / .5kg .6m pi
n = 38.2 rpm.............Answer for (b)

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