It can be shown that if a pendulum mass on a string is dropped from a height as

Question

It can be shown that if a pendulum mass on a string is dropped from a height as shown the final velocity will be Squareroot 2gh. (we did this in the energy lab) This is because all of the mass is located at the end of the string giving it a moment of inertia of mL^2. If instead a solid rod of the same mass and length was allowed to swing the same distance, and knowing the moment of inertial to be 1/3 mL^2 what is the velocity of the very tip of the rod at the bottom? (if you want you can use a mass of 1 and a length of 1, )

Explanation / Answer

using the potential energy is PE = m g h

when it decreases in the PE is PE = m g h/2

and

the kinetic energy is KE = 1/2 m v2

KE = PE

1/2 m v2 = m g h/2

1/2 v2 = g h/2

v2 = g h

v = ( g h )1/2

so the velocity at the bottom is v = ( g h )1/2

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