Answer to Question #290259 in Mechanics | Relativity for Blessing

Question

A solid rigid body rotating about an axis has a mass of 20kg and a radius of 2m from the axis of rotation. If the angular velocity is 25 rad/s,calculate the rotational kinetic energy

Answer 1

Explanation & Calculation

• To begin with, calculate the rotational inertia of the body about that axis,

$\qquad\qquad \begin{aligned} \small I&=\small mr^2\\ &=\small 20\,kg \times (2\,m)^2\\ &=\small 80\,kgm^2. \end{aligned}$

• Then, calculate the rotational; kinetic energy of the body as follows.

$\qquad\qquad \begin{aligned} \small E_k&=\small \frac{1}{2}I \omega^2\\ &=\small 0.5\times80\,kgm^2\times(25\, s^{-1})^2\\ &=\small 25000\,J\\ &=\small 25\,kJ \end{aligned}$