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The eel has a certain amount of rotational kinetic energy when spinning at 14 spins per second. If it swam in a straight line instead, about how fast would the eel have to swim to have the same amount of kinetic energy as when it is spinning

Respuesta :

Answer:

[tex]v=\frac{28\pi R}{\sqrt{2} }[/tex] m/sec

Explanation:

According to the question

[tex]\frac{1}{2}I\omega^2=\frac{1}{2} mv^2[/tex]

\omega= angular velocity = 14 spins per sec

I= MOI of the spinning eel= 0.5mR^2

m= mass of eel

v= linear velocity of eel.

[tex]\frac{1}{2}0.5mR^2\omega^2=\frac{1}{2} mv^2[/tex]

solving for v in the above equation we get

[tex]v=\sqrt{\frac{R^2\omega^2}{2} }[/tex]

now \omega in radians = 14 rev/sec×2π  radian/rev= 28π radian/sec

value of radius is not provided in the question

therefore we get

[tex]v=\frac{28\pi R}{\sqrt{2} }[/tex]