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 = 3π/4 km, r = 2 km, t = 4 sec

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve for Omega using the formulas. Omega equals theta divided by T and S equals R theta. We're also told that S equals five pi divided by seven kilometers, R equals nine kilometers and T equals two seconds. Our answer choices are answer choice. A pi divided by 63 radians per second. Answer choice B pi divided by 18 radians per second. Answer choice C five pi divided by 63 radiance per second and answer choice D five pi divided by 126 radiance per second. So let's see what we're trying to find. We're looking for Omega that's in the first formula. Omega equals theta divided by T. Well, we don't know theta yet in the numerator, but we do know t in the denominator, that's two seconds. So we can try to figure out what theta is. That's in the other formula as well. S equals R theta. So let's see what we can fill in there. S is five pi divided by seven kilometers, that's equal to R which is nine kilometers theta we want to solve for theta. So it's a, we'll divide both sides by nine kilometers. Since we've got a fraction within a fraction, I'm going to rewrite this five pi divided by seven kilometers divided by, with the division symbol nine kilometers. And when we're dividing fractions, we can multiply by the reciprocal. So we'll have five pi divided by seven kilometers multiplied by one divided by nine kilometers. And now our kilometers cancel out and we can multiply straight across our numerators. Five pi multiplied by one. So that's five pi divided by seven, multiplied by nine, that's 63. Now, this is our theta that we're talking about and theta is measured in radiance. So our units here are radiance. Now, we can plug that in for theta in the first formula. So Omega is equal to five pi divided by 63 radians divided by two seconds. Again, a fraction within a fraction. We can, we can rewrite this five pi divided by 63 radians divided by two seconds is the same as five pi divided by 63 radians multiplied by one, divided by two seconds. And in the numerators, we just have five pi radiance and in the denominators, 63 multiplied by two is 126 and then we have the unit seconds. So our Omega is five pi divided by 126 radians per second. We look at our answer choices and this matches with answer choice. D well 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 = 3π/4 km, r = 2 km, t = 4 sec

Key Concepts

Angular Displacement (θ)

Angular Velocity (ω)

Arc Length (s)

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