https://blog.saya.kazv.moe 2022-04-20T20:56:38.000Z https://blog.saya.kazv.moe/2022/04/20/Rotational-vs-Translational-Kinetic-Energy/ <p>$$E_{rotational} = \frac1 2 I*\omega^2$$</p> <p>Consider a particle with mass $m$ revolving about a pivot $O$ with a constant distance $r$ between them. It is revolving with constant angular velocity $\omega$ Its moment of inertia is: $$I = m<em>r^2$$ Thus $$E_{rotational} = \frac1 2 m</em>r^2*\omega^2$$</p> <p>Since $\omega = \frac v r$</p> <p>$$E<em>{rotational} = \frac1 2 m<em>r^2</em>\frac{v^2}{r^2}$$ $$E</em>{rotational} = \frac1 2 m*v^2$$</p> <p>We could see this looks exactly as the Translational Kinetic Energy, which is:</p> <p>Of an any given moment, the instantaneous velocity of this particle is $v$, so we can calculate its Translational Kinetic Energy with the formula</p> <p>$$E_{translational} = \frac1 2 m*v^2$$</p> 2022-04-20T20:56:38.000Z https://blog.saya.kazv.moe/2022/04/20/GSoC-Blog-Placeholder/ <p>placeholder</p> 2022-04-20T06:59:11.000Z https://blog.saya.kazv.moe/2022/04/18/arata/ <p>sinsekaidesu!</p> 2022-04-18T22:24:25.000Z