Answer to Question #137947 in Field Theory for Afraid

Question

A small body of mass m = 0.10 kg moves in the reference frame rotating about a stationary axis with a constant angular velocity w = 5.0 rad/s. What work does the centrifugal force of inertia perform during the transfer of this body along an arbitrary path from point 1 to point 2 which are located at the distances r1 = 30 cm and r2 = 50 cm from the rotation axis?

Answer 1

solution

work done by centrifugal force can be given as

$W=\int^{r_2}_{r_1}m\omega^2rdr$

so

$W=\frac{1}{2}m\omega^2(r_2^2-r_1^2)$

$W=\frac{1}{2}\times0.1\times5^2\times(0.5^2-0.3^2)$

$W=0.20J$

so work done by centrifugal force is 0.20J.