Find the linear speed v for each of the following.

Question

a point on the edge of a flywheel of radius 2 m, rotating 42 times per min

Accepted Answer

Welcome back. I am so glad you're here. We are told about a revolving door at a building in Manhattan. Going to draw this as though we're looking at it from a bird's eye point of view. Looking from the top down, there are the doors and they are revolving in a circle. It rotates 15 times. So that's 15 revolutions per minute if a point on its edge, so we can draw this at the edge of one of the doors is 1.5 m away from the center of the door. What is the linear speed of this point? So we're looking for linear speed. V. Our answer choices are answer choice, a 45 pi meters per minute. Answer choice, B 15 pi meters per minute, answer choice, C 30 pi meters per minute and answer choice D 25 pi meters per minute. We recall from previous lessons that linear speed can be found if we take radius multiplied by omega the angular speed. So R multiplied by omega and our radius here is given to us the distance from the edge to the center of the door is 1.5 m. But how about our omega our angular speed. Well, we're close. We're given that we have 15 revolutions per minute revolutions per minute is not our angular speed, but our angular speed is given in radians per unit of time. And we can convert from revolutions to radiance. We recall from previous lessons that one revolution, one time around the circle is equal to two pie radiance. So we can use unit conversion to get our revolutions to cancel out. We'll put two pi radians in the numerator divided by one revolution, our revolution units cancel out multiplying straight across. We've got 15, multiplied by two pi is 30 pi that's radiance per and in the denominator we just have minutes. So our angular speed is 30 pi radiance per minute. And now we have our and Omega we can solve for V our linear speed. So we'll say V equals instead of R 1.5 m multiplied by Omega which is 30 pi radiance per minute. Multiplying straight across 1.5 multiplied by 30 pi is 45 pi and then our units, we've got meters in the numerator. We also have radiance but linear speed is expressed in terms of distance divided by time. So we will disregard the radiance for our answer. We have meters per minute and that is our linear speed. 45 pi meters per minute. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

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Find the linear speed v for each of the following.

a point on the edge of a flywheel of radius 2 m, rotating 42 times per min