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
Explanation & Calculation
I=mr2=20 kg×(2 m)2=80 kgm2.\qquad\qquad \begin{aligned} \small I&=\small mr^2\\ &=\small 20\,kg \times (2\,m)^2\\ &=\small 80\,kgm^2. \end{aligned}I=mr2=20kg×(2m)2=80kgm2.
Ek=12Iω2=0.5×80 kgm2×(25 s−1)2=25000 J=25 kJ\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}Ek=21Iω2=0.5×80kgm2×(25s−1)2=25000J=25kJ
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