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.

r = 6 cm, ω = π/3 radians per sec, t = 9 sec

Accepted Answer

Welcome back. I am so glad you're here. We are asked to solve for S using the formulas. Omega equals theta divided by T and S equals R theta. We're given that R equals 20 centimeters. Omega equals three pi divided by four radians per second and T equals 12 seconds. Our answer choices are answer choice. A 196 pi centimeters. Answer choice, B 72 pi centimeters. Answer choice, C 90 pi centimeters and answer choice. D 180 pi centimeters. All right. So let's see what we can fill in and what we're looking for. We're looking for S S as in this second formula. S is equal to R multiplied by theta. We know RR is 20 centimeters, but we don't know theta yet. So lets go in search of theta, theta can be found in the first formula. Omega equals theta divided by T. We know Omega and we know T so we can solve for theta plugging in Omega is three pi divided by four radians per second. It's equal to theta are unknown, divided by T which is 12 seconds. In order to get theta by itself, we multiply both sides by 12 seconds on the left, our seconds cancel out. And so now multiplying across our numerators, we have 12 multiplied by three pi and that's going to be 36 pie. And we still have radians. And in the denominator, we just have four and no units. We can simplify this. 36 pi divided by four is nine pi. So we have nine pi radiance is our theta. So now we can use that and substitute that back into our formula. S equals R multiplied by theta. So our was 20 centimeters and theta is nine pi radiance multiplying 20 by nine pi that's 180 P. And for our units S is the length of the arc. So that's just expressed in terms of distance. So we're just going to hang on to centimeters. It's not expressed in terms of radiance. So there is our s 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.

r = 6 cm, ω = π/3 radians per sec, t = 9 sec

Key Concepts

Angular Displacement and Angular Velocity

Arc Length Formula

Substitution to Relate Variables in Rotational Motion

Watch next