Use the formula v = r ω to find the value of the missing ...

Question

Use the formula v = r ω to find the value of the missing variable.

v = 12 m per sec, ω = 3π/2 radians per sec

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve for R by using the formula V equals R. Omega. We're given that V equals 21 m per second and that Omega equals seven pi divided by six radians per second. Our answer choices are answer choice, A 18 divided by pi meters. Answer choice B six divided by pi meters. Answer choice C three pi meters and answer choice D nine pi meters. All right. So we're solving for R let's fill in what we know to the formula V on the left hand side is 21 m per second. That's equal to on the right. We don't know R that's multiplied by Omega is seven pi divided by six radians per second. We want to get R by itself. So what we need to do is divide both sides by the what Omega is seven pi divided by six radians per second. But because we have fractions here, we can multiply by the reciprocal of those fractions in order to cancel them out. So we're multiplying both sides by six, divided by seven pi seconds per radiance and doing that to both sides. And now on the right hand side, all of that cancels out. And on the left, we can see that our seconds are going to cancel out. And so multiplying straight across the numerators, six multiplied by 21 is 126. Then we still have meters. And in the denominators, we just have seven pi for the numbers we have radiance there. However, R is expressed in terms of distance, it's not expressed in terms of radiance. So we can leave that off. And now we can just simplify 126 divided by seven is 18. So we have 18 divided by pi meters. And there is our R we look at our answer choices and that matches with answer choice. A well done. We'll catch you on the next one.

Use the formula v = r ω to find the value of the missing variable.

v = 12 m per sec, ω = 3π/2 radians per sec

Key Concepts

Linear Velocity (v)

Angular Velocity (ω)

Relationship Between Linear and Angular Velocity (v = rω)

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