In Exercises 79–80, express each angular speed in radians per sec...

Question

In Exercises 79–80, express each angular speed in radians per second.

6 revolutions per second

Accepted Answer

Welcome back. I am so glad you're here. We are told that the given angular speed is in revolutions per second. Write it in radiance per second. Our given angular speed is 92 revolutions per so divided by second. Our answer choices are answer choice. A 46 pi radians per second. Answer choice B 184 pi radians per second answer choice. C 100 excuse me, 368 pi radiant per second and answer choice D 224 pi radiant per second. All right. So we've got revolutions per second and we want radians per second. So the question here is how many radians are in a revolution? This is essentially just unit conversion. So we know from previous lessons that one revolution is equal to two pi radians. And because those two things are equal, we can write them as a ratio. So we can multiply our 92 revolutions divided by second or revolutions per second by and then we want our revolution units to cancel out. So we'll put two pi radiant in the numerator and that's divided by one revolution. And then our revolution units will cancel out and we will have radiant in the numerator and seconds in the denominator. So we'll have radians per second, which is just what we want. So now doing the multiplication, the only multiplication is in the numerators where we have 92 multiplied by two pi and that is 184 pi and then we have our units which are radians per second. So 184 pi radians per second, we look at our answer choices and this matches with answer choice. B well done. We'll catch you on the next one.

In Exercises 79–80, express each angular speed in radians per second. 6 revolutions per second

Key Concepts

Angular Speed

Revolutions to Radians Conversion

Unit Circle

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