Question #290259

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


1
Expert's answer
2022-01-25T06:50:35-0500

Explanation & Calculation


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

I=mr2=20kg×(2m)2=80kgm2.\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.

Ek=12Iω2=0.5×80kgm2×(25s1)2=25000J=25kJ\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}



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