Consider a rope of mass M and length L rotating on top of a table in a horizontal
plane. One of the ends of the rope is fixed and does not move. The rope moves in a circle with angular frequency w. What is the kinetic energy of the rope?

Question

Consider a rope of mass M and length L rotating on top of a table in a horizontal
plane. One of the ends of the rope is fixed and does not move. The rope moves in a circle with angular frequency w. What is the kinetic energy of the rope?

anonymous · Answer

@ganeshie8

ganeshie8 · Answer

In your notes, lookup the `moment of inertia` of a rod of mass M and length L

ganeshie8 · Answer

Kinetic energy = 1/2 * (moment of inertia) * (angular velocity)^2

anonymous · Answer

The answer I am getting is $$KE= \frac{ 1   }{ 2} I \omega^2$$

ganeshie8 · Answer

looks good, just plugin the value of $I$ for the rope

anonymous · Answer

What would that be? :O Because I replaced mr^2 with I.

ganeshie8 · Answer

It seems $I = \dfrac{ML^2}{3}$ for the rope with one end as axis of rotation https://en.wikipedia.org/wiki/List_of_moments_of_inertia

anonymous · Answer

Okay. But how is this value of I derived?