A model of a helicopter rotor has four blades, each 3.40 m long f...

Question

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. (b) What is the radial acceleration of the blade tip expressed as a multiple of g?

Accepted Answer

Welcome back everybody. We are given a ceiling fan and this ceiling fan makes a circle when it rotates, go ahead and draw your ceiling fan and they're here. And these will be, it's a Now we are told that the circle that the ceiling fan makes as a radius of cm or .6 m were also told that it has a revolution or minute Equal to 1200. And we're also told that there's going to be this little tiny mass at the end of one of the blades. And we're told that the mass is going to be one g or .001 kg. So we are then tasked to find what the radial acceleration is of this little particle right here. Well, the formula for radial acceleration is going to be b squared or tangential velocity over the radius. But what is our V. Here? Well, there's another formula that R V is equal to two pi times the radius, all divided by the period of rotation, but we don't have the period. So we'll need one more formula that says, our period is equal to one divided by the revolutions per second of our object. So let's go ahead and start from the end here and work our way backwards. Our period is going to be equal to one over our revolutions per second while we're given revolutions per minute. So to get per second we're just going to divide that by 60. When you plug this into your calculator, you get that the period is .05 seconds. Great. Now our velocity is going to be equal to two pi times. Uh sorry our let's see here, our radius of .6 over Our period of 0.05 seconds. Looking this into your calculator, you get that are tangential velocity is 75.4 m/s. Now that we have our velocity, we are ready to find our centripetal acceleration. We have that A. C. Is equal to our velocity squared, so 75.4 squared all over our radius of 0.6. Which when you plug this into your calculator, you get that. Our acceleration is 9.5 times 10 to the third meters per second squared corresponding to our answer choice of B. Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.

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