The formula ω = θ/t can be rewritten as θ = ωt. Substituting ω...

Question

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

s = 6π cm, r = 2 cm, ω = π/4 radian per sec

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve for tea using the formulas. Omega equals theta divided by T and S equals are multiplied by theta. We're given that S equals 21 pi centimeters, that R equals six centimeters and that Omega equals pi divided by two radians per second. Our answer choices are answer choice. A 14 seconds. Answer choice, B seven seconds, answer choice C three divided by two seconds and answer choice D seven pi seconds. All right. So we're looking for T, where is that in our formulas? It's in the denominator of this first formula Omega equals theta divided by T. So what else do we know in that formula? We know Omega that is pi divided by two radians per second that equals while we don't know theta in the numerator. And T is what we're looking for in the denominator. So where else can we find theta? Well, that's not a given, but it is in the second formula S equals R multiplied by theta. So let's see what else we know in that one s on the left is 21 pi centimeters that equals R is six centimeters multiplied by theta. Well, we can solve for theta. Now, we'll divide both sides by six centimeters. And on the right, six centimeters cancels out on the left, the centimeters cancels out. And we just have 21 pi divided by six, we can reduce that. They're both divisible by three. So we can have seven pi divided by two. That's our theta. But it's important to note that theta is measured in terms of radiance. So that's our unit for theta. Now, we can use that and plug it back into our formula on the left hand side so that we can solve for T. So we'll have pi divided by two radians per second equals. And in the numerator, we have seven pi divided by two radians. That's all divided by T. Now, our goal is to solve for T, let's get T out of the denominator. We'll multiply both sides by T and on the right, the teas cancel out, we want to get the T by itself on the left. And in order to do that, we can multiply by the reciprocal of all of those fractions. So we'll have T multiplied by our omega is pi divided by two radians per second. And the reciprocal of that is two divided by pi seconds per radium. That's equal to our theta which is seven pi divided by two radians. And now multiplying that by the reciprocal of our omega two divided by pi seconds per radiant. And now some really fun canceling out everything on the left except for the tea cancels out and on the right. Our pies cancel out our radiance, cancel out our twos cancel out and we are left with a T value of seven seconds. We look at our answer choices and this matches with answer choice B while done. We'll catch you on the next one.

The formula ω = θ/t can be rewritten as θ = ωt. Substituting ωt for θ converts s = rθ to s = rωt. Use the formula s = rωt to find the value of the missing variable.

s = 6π cm, r = 2 cm, ω = π/4 radian per sec

Key Concepts

Angular Displacement (θ)

Angular Velocity (ω)

Arc Length (s)

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