8. (5 points) solve the following equation for v. f_c = m v^2 / r

Explanation:

Step1: Isolate $v^{2}$

Multiply both sides by $r$ and divide by $m$ to get $v^{2}=\frac{F_{c}r}{m}$.

Step2: Solve for $v$

Take the square - root of both sides. Since we are solving for a physical quantity, we consider both positive and negative roots. So $v = \pm\sqrt{\frac{F_{c}r}{m}}$.

Answer:

$v=\pm\sqrt{\frac{F_{c}r}{m}}$