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I have been learning about oscillating bodies and recently stumbled upon physical pendulums. Now the problem is i don't understand about which axis is the MOI calculated while finding the TIME PERIOD(T)

for example if i have a curved surface of radius=$R$ with a small ball of radius $r$ (please ignore the blue line ,the ball is not connected to any point and the ball is rolling without slipping) . enter image description here

so my doubt here is should i calculate the MOI along the centre of mass or the edge of the ball /:)

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You can take the moment of inertia about either the C of M or the fixed point --- as long as you take care to calculate the torque about your chosen point. Calculating the torque about the C of M is perhaps a bit harder as you need to find the reaction force at the fixed point.

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  • $\begingroup$ can u elaborate ? $\endgroup$
    – user287374
    Commented Feb 27, 2021 at 12:50
  • $\begingroup$ , how do i calculate the restoring force along the COM $\endgroup$
    – user287374
    Commented Feb 27, 2021 at 12:51
  • $\begingroup$ What do you mean "the restoring force along the C of M" This means nothing to me! Just draw the free-body diagram. Equate the sum of forces to mass times acceleration and torques to rate of change of angular momentum. All this must be explained in you textbook, surely? $\endgroup$
    – mike stone
    Commented Feb 27, 2021 at 12:57
  • $\begingroup$ based on wht i have learnt i am supposed to find the restoing force(forcing causing the oscillation in this case restoring torque, $\endgroup$
    – user287374
    Commented Feb 27, 2021 at 13:00
  • $\begingroup$ You drawing is far too vague to be of much help. Is the ball rolling on the surface? Is it swinging from the string and there is no actual surface? Are you supposed to worry about the moment of inertial of the Ball about its C of M, or can you treat it as a point mass? Is it to be treated as a rigid compound pendulum? All this will be stated in your question, but you have not bothered to tell us. $\endgroup$
    – mike stone
    Commented Feb 27, 2021 at 13:07