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?

Video transcript

Welcome back everybody. We are making observations about a ceiling fan and we are told that the ceiling fan has a radius of rotation of 60 cm and or .6 m. Now we are told that it also rotates. Its rotations per minute is At full speed. Now we have a little particle that is resting at the edge of these fan blades are on the circle generated by the radius. We are told that the mass of it is one g or .001 kg. And we are tasked with finding what the radial acceleration is experienced by the particle. Now we have a formula for this. This is gonna be equal to the velocity squared over the radius. But what is our velocity here? More velocity is going to be equal to two pi times our radius all over T. But what is T here? Well, T. Is in reference to the speed right at which the the fan blades are rotating the period here. Now the period is just going to be one over the frequency. But the frequency is in. Let's see here, revolutions per second. So we'll have to convert this to find T. But once we find T, we'll find V. And once we find V, we'll find a C. So let's start from the beginning here. First and foremost, we need to convert our revolutions per minute. Two revolutions per second. So we have revolutions per one minute and in one minute we have seconds. So this is going to equal revolutions per second. Great. So now let's go ahead and find T. T. is going to be one over r frequency that we just found of 20. This gives us 0.05 seconds. With that we can go ahead and find our velocity here. Which is going to be two pi times R radius of 20.6. All divided by 0.5. Giving us a velocity of 75.4 m per second. Now that we have our velocity we can find our angular. Sorry, our centripetal acceleration here we have a C. Is equal to 75.4 squared, all divided by 0.6. Giving us a final answer of 9.5 times 10 to the third meters per second squared corresponding to our answer choice of B. Thank you all so much for watching. Hope this video helped. We will see you all in the next one.