Answer:
72 J
Explanation:
Total kinetic energy will be tge sum of rotational and translational energy.
Rotational kinetic energy is given by [tex]0.5I\omega^{2}[/tex] where I is moment of inertia which is given by [tex]mr^{2}[/tex] and here m is mass, r is radius. Also, [tex]v=\omega r[/tex] hence making \omega the subject then [tex]\omega=\frac {v}{r}[/tex] where v is the velocity.
Rotational kinetic energy=[tex]0.5I\omega^{2}=0.5mr^{2}\times(\frac {v}{r})^{2}= 0.5mv^{2}[/tex]
This is same as the formula for translational kinetic energy which is given by [tex]0.5mv^{2}[/tex]
Therefore, total kinetic energy= [tex]0.5mv^{2}+0.5mv^{2}=mv^{2}[/tex]
Substituting m with 2 kg and v with 6 m/s then total energy will be [tex]2\times 6^{2}=72 J[/tex]
