If I hang a small cylindrical/spherical object with a string, I get a pendulum. When I swing it, the object mostly rotates about its axis. What effect does this rotation have on the time period of the pendulum? Can we find out the effect quantitatively?
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I have never did research on this valuable question.
Therefore I am giving you a medal for this.
I think rotation of pendulum about its own axis is not affected by gravity so no change in time period is considered.
i dont know how to prove it theoreticaly but considering rotation of sphere along its own axis,the thread which supports the bob gets twisted thereby affecting the value of effective tension in string and also the LENGTH of thread gets reduces due to twisting
so its does affect the time period of the pendulum
thank u @shayaan. @salini maybe u r right. actually i stumbled upon this question while thinking of an idea that a pendulum could behave as an altimeter. I just measure the time period accurately and through equations get the height above sea level i am at. But since time period changes very slightly with even a great change in height, i need to be very accurate in measuring it. i tried to measure time period of my pendulum with and without rotation, and it appears to be lower in the case of rotation.
but a theoretical equation of some sort would be great. I am currently working on it too/
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If the pendulum is rotation, it has angular momentum. When the pendulum swings, that angular momentum changes direction. Therefore a torque was applied and work was done. With every swing, one way or another, work is done and mechanical energy is lost.
Hence for every oscillation, the amplitude will decrease.
hey i have been thinking about this and i think this is a satisfying explanation
when the bob begins to rotate,its total kinetic energy is being shared by rotional kinectic energy and translational(linear) kinetic energy
it is only the translational(linear) kinetic energy part that is being converted to mgh(gravitaional potential energy)
and that reduced height reached clearly explains why the time period reduces
for maximum undersatnding take alook at this lecture at part 47:05
If you had an gyroscope at the end of the pendulum that could maintain its axis of rotation and hence have constant angular momentum, your explanation would be right.
What's important about the situation described is that the axis of rotation is constantly changing with every oscillation. Hence angular momentum DOES change, that external torque IS applied, that work IS done in applying this torque, and this is the reason that energy is lost.