Question

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

Answer 1

`v=(28\pi R)/(√(2) )` m/sec

Step-by-step explanation:

According to the question

`(1)/(2)I\omega^2=(1)/(2) mv^2`

\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.

`(1)/(2)0.5mR^2\omega^2=(1)/(2) mv^2`

solving for v in the above equation we get

`v=\sqrt{(R^2\omega^2)/(2) }`

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

`v=(28\pi R)/(√(2) )`