Centripetal Acceleration calculation help

In summary, the centripetal acceleration at the tip of a 4.00 m long helicopter blade rotating at 300 rpm is 3948.87 m/s^2. The linear speed of the tip is 125.28 m/s, which is slower than the speed of sound (340 m/s). It is not possible for a propeller-driven aircraft to move at supersonic speeds due to the limitations of the blades.
  • #1
nautica
a) calculate the centipetal acc at the tip of a 4.00 m long helicopter blade that rotates at 300 rpm.

300 rpm = 31.42 rad/s = w

Centrip Acc = rw^2

Ac = (3.41 rad/s)^2 * 4 m

Ac = 3948.87 m/s^2

b)compare linear speed of the tip with the speed of sound which is 340 m/s

v=rw

v = 4m * (31.42 rad/sec) = 125.28 m/s

So the blades are slower than the speed of sound.

This does not sound right to me I figured the blades would be faster - but maybe just not at the tip?

Thanks
Nautica
 
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  • #2
OK up to here, I think...
Originally posted by nautica
Ac = 3948.87 m/s^2
But how do you arrive at this figure? - Seems much too large to me...
v=rw
v = 4m * (31.42 rad/sec) = 125.28 m/s
So the blades are slower than the speed of sound.
This does not sound right to me I figured the blades would be faster - but maybe just not at the tip?
IMO, your math is correct here. Not sure, but I think helicopters have been around since the 1920's or so, when no aircraft engineer was even close to handling supersonic speeds... Still those machines worked, didn't they? Another thing, I believe it's not possible to move supersonic with any propeller-driven aircraft because the blades are just not allowed to move supersonic - turbulence & friction would lead to destruction... Just compare a helicopter's sound to that of a whiplash (where the tip does reach supersonic) - it's very different, much smoother isn't it? ... Enough for now.
 
  • #3
Sorry, it was a typo, should have been 31.42

Thanks
Nautica
 

1. How is centripetal acceleration calculated?

Centripetal acceleration can be calculated using the formula a = v^2/r, where a is the acceleration, v is the velocity of the object, and r is the radius of the circular motion.

2. What is the difference between centripetal acceleration and centrifugal acceleration?

Centripetal acceleration is the acceleration towards the center of a circular motion, while centrifugal acceleration is the apparent outward acceleration experienced by an object in a rotating reference frame. Centrifugal acceleration is not a real force, but rather a result of the object's inertia.

3. How does centripetal acceleration affect the motion of an object?

Centripetal acceleration causes an object to continuously change its direction, but not its speed, as it moves in a circular path. This acceleration is responsible for keeping the object in its circular motion, preventing it from moving in a straight line.

4. Can centripetal acceleration be negative?

Yes, centripetal acceleration can be negative if the object is slowing down or changing direction in a way that causes the acceleration to point in the opposite direction of the object's motion.

5. How is centripetal acceleration related to centripetal force?

Centripetal acceleration and centripetal force are directly related, as the force required to keep an object in circular motion is equal to the mass of the object multiplied by its centripetal acceleration, according to the formula F = ma.

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