Question

A small body of mass $m=0.10kg$ moves in the reference frame rotating about a stationary axis with a constant angular velocity $\omega =5.0rad/s$. If the work done by the centrifugal force of inertia during the transfer of this body along an arbitrary path from point 1 to point 2 which are located at the distances $r_1=30cm$ and $r_2=50cm$ from the rotation axis is $\frac{x}{10}J$. Find $x$.

Answer 1

Centrifugal force of inertia is directed outward along radial line, thus the work is
$W={\int }_{r_1}^{r_2}m{\omega }^{2}rdr$

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

$=0.20J$ (On substitution)