Question

Calculate the kinetic energy of a body, rotating about an axis with uniform angular velocity.

Answer 1

Rotational Kinetic Energy

Suppose a body is rotating with uniform angular velocity co relative to the axis YY’. Every particle of the body will have same angular velocity but different linear velocity. Suppose, a particle of mass $m_1$ is at a distance $r_1$ from the rotational axis. Since, the linear velocity of each particle is the multiplication of the angular velocity with the distance from the rotational axis. Hence, linear velocity of the particle.

$v_1=r_1\omega$

and its kinetic energy

$=\frac{1}{2}{m}_1{v}_1^2=\frac{1}{2}{m}_1(r_1\omega {)}^2=\frac{1}{2}{m}_1{r}_1{\omega }^2$