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There is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 12 cm. When the cylinder is rotating at 2.0 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall?
19$m / s^{2}$
Physics 101 Mechanics
Chapter 5
Dynamics of Uniform Circular Motion
Newton's Laws of Motion
Applying Newton's Laws
Cornell University
University of Michigan - Ann Arbor
University of Washington
McMaster University
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in this problem, we have to find the angular acceleration of the kitchen device huge for drying lettuce leaves and were given the radius of the device takes one second to complete two revolutions. So from that second piece of information, we can actually get it very well that we need, which is t the period. Now the period describes the amount of time that it takes for an object complete one full revolution. And since we know that there's two revolutions in one second, it must take half a second to complete a full revolution. From here, we can use the equation that we know for tea, which is two pi over the angular velocity, Um which will make up Omega is equal to the over our. So we can rewrite tease we have before as to tie our over me. So from here we can rewrite the equation for V which is going to be too. Hi are over tea. And now, in order to find the angular acceleration, we can plug on a miracle values into this equation. Here. Alfa is V squared over R. So when we plug in and we simplify, we get that Alfa is equal to four pi squared R over t's weird and now all that's left to do is plugging our numerical values. We get four pi squared times 0.12 meters all over 1/2 2nd squared move to a new whiteboard cause woke up pretty crowded and that is equal to 18.95 with units of meters per second squared which we can round 2 19 um, meters per second squared and there's your answer.
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