Use the formula $\nu=\mathrm{r} \omega$ to find the value of the missing variable. $r=25 m, \omega=\frac{4 \pi}{5}$ radians per sec The missing variable is $\nu=$ $\mathrm{m}$ per sec. (Type an exact answer.)

Step 1 ：Given the formula for linear velocity, \(\nu = r \omega\), where \(r = 25 m\) is the radius and \(\omega = \frac{4 \pi}{5} rad/sec\) is the angular velocity.

Step 2 ：Substitute the given values into the formula: \(\nu = 25 m * \frac{4 \pi}{5} rad/sec\).

Step 3 ：Simplify the expression to find the value of \(\nu\).

Step 4 ：Final Answer: \(\boxed{62.83} m/sec\).