Question

A 54-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 200 rpm at the end of 12 s .

Part A

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

Express your answer to two significant figures and include the appropriate units.

F =

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Part 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 12 seconds?

Express your answer to two significant figures and include the appropriate units.

ω =

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Answer 1

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 = 3.14* 0.5kg 0.54m *200rpm / 360*12s
F = .040N

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*12s .04N / .5kg *0.54m* pi
n = 50.95 rpm