A model of a helicopter rotor has four blades, each of length 3.50 from the central shaft…
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A model of a helicopter rotor has four blades, each of length3.50 from the central shaft to the blade tip. The modelis rotated in a wind tunnel at a rotational speed of 510 .
(a) What is the linear speed of the bladetip?
(b) What is the radial acceleration of the bladetip expressed as a multiple of the acceleration of gravity,?
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Technifi Expert’s Answer:
r = 3.5m
ω = 510rpm.
We can convert the rotational speed to rps (rotations persecond)
Circumference is Pi x D C = πD
That’s the distance the tip travels through one rotation, we have8.5 in one second.
Radial acceleration is also centripetal acceleration.
The acceleration a may be negative which would result in-9983.105. If we then divide it by g = -9.8 m/s, we achieve the same result. Use your own discretion on that part.
linear speed is v = rw where r = radius and w = angular velocity
Now 510 rpm = 510 x 2pi radians per min = 510 x 2pi/60 rads/sec = w
w = 53.4 rads/s
v = r w = 3.5 x 53.4 m/s = 186.9 m/s
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