Use the formula $v=r \omega$ to find the value of the missing variable. $r=20 m, \omega=\frac{3 \pi}{4}$ radians per sec The missing variable is $\nu=$ m per sec. (Type an exact answer using pi)

Step 1 ：We are given the formula for velocity in circular motion, which is \(v = r \omega\), where \(r\) is the radius and \(\omega\) is the angular velocity.

Step 2 ：We are given that \(r = 20\) m and \(\omega = \frac{3 \pi}{4}\) radians per sec.

Step 3 ：Substitute these values into the formula to find the value of \(v\).

Step 4 ：\(v = 20 \times \frac{3 \pi}{4}\)

Step 5 ：\(v = 15 \pi\) m per sec.

Step 6 ：Final Answer: The missing variable, the velocity (v), is \(\boxed{15 \pi}\) m per sec.