Question

use the formula v = rω to find the value of the missing variable. v = 12 m per sec, ω = $\frac{3pi}{8}$ radians per sec the missing variable is r = (simplify your answer. type an exact answer, using π as needed.)

Explanation:

Step1: Rearrange the formula for r

Given $v = r\omega$, we can solve for $r$ by dividing both sides by $\omega$. So $r=\frac{v}{\omega}$.

Step2: Substitute the given values

Substitute $v = 12$ and $\omega=\frac{3\pi}{8}$ into the formula for $r$. We get $r=\frac{12}{\frac{3\pi}{8}}$.

Step3: Simplify the expression

$r = 12\times\frac{8}{3\pi}=\frac{96}{3\pi}=\frac{32}{\pi}$ m.

Answer:

$\frac{32}{\pi}$ m