Find the angular speed ω for each of the following.

Question

a wind turbine with blades turning at a rate of 15 revolutions per minute

Accepted Answer

Welcome back. I am so glad you're here. We are asked to calculate the angular speed omega of a ride in an amusement park in Ontario, Canada. The ride operates at 12 revolutions per minute. Our answer choices are answer choice. A four radians per minute. Answer choice B eight pi radians per minute. Answer choice. C 24 Pi Radians per minute and answer choice. D 12 pie radians per minute. All right, we know that angular speed is expressed in terms of theta divided by T it's in radiance per unit of time and we have something very similar to that. We're told that we have an amusement park ride operating at 12 revolutions per minute, but revolutions are not the same as radiance, but we can convert between the two. We recall from previous lessons that one revolution is equal to two pi radians once around the circle is two pi radians. So we can use unit conversion in order to get this in terms of radians per unit of time. So we'll multiply our 12 revolutions per minute by we'll put two pi radians in the numerator because we want to cancel out the one revolution in the denominator. Now, our revolutions cancel out and we multiply straight across 12, multiplied by two. Pi Radians gives us 24 pi Radians. And in the denominator, all we have left is minutes. So it's radians per minute and there is our angular speed. 24 pi radians per minute. We look at our answer choices and that matches with answer choice. C well done. We'll catch you on the next one.

Find the angular speed ω for each of the following.

a wind turbine with blades turning at a rate of 15 revolutions per minute

Key Concepts

Angular Speed (ω)

Conversion between Revolutions and Radians

Units and Dimensional Analysis

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