What is the centripetal force when instead of a mass point we have a physical rotating body? I was wondering what is the centripetal force of a body rotating in a circular motion. I know that the centripetal force of a point mass is $mv^2/r$. I only have done an introductory physics class so I can not find the answer.
 A: Centripetal force is the force which keeps a body on a circular path. It is not a new force.
Any force that acts towards the center of that circular path is your centripetal force. For example in case of earth and sun , the gravitational force is the centripetal force on the earth and it is just
$ mg = \frac{mv^2}{r} $
Where $r$ is the distance between the center of mass of the revolving body and the point about which it is rotated. Changing shape will only affect this distance and nothing else.
We actually don't need to prove that changing shape i.e. center of mass will affect the formula , the formula is itself defined to be force between the center of masses. So changing shape will affect the distance between the center of masses. For example , if a hemispherical or a triangular object is being rotated with a string then we will have to use the extra distance between the center of mass and the point where the string is attached to the body i.e.
$T = \frac{mv^2}{r + d_{centre of mass }}$
, Where $T$ is the tension force  and $r$ is the distance between the fixed point and the point where body and string are attached.
And since $d_{center of mass}$ will be different for different shapes the force will be different.
A: you probably come to that in your cours later.
for short:  you take all masses with the same r  for them its just your formula, then you have to add all the forces for the masses with different r. If you know what integrating is you integrate over all radii. For simple forms of bodies you calculate their "moment of inertia" I  -look this up- and then you know  calculate the force.
but for a firs approximation you take r to the center of mass and use the formula for a pointmass.
A: 
I was wondering what is the centripetal force of a body rotating in a
circular motion.

It does not only apply to point masses. You can apply it to the center of mass of a rotating body.
Refer to the figure below of a figure skating pair. The woman skater is moving in a circular path around the male skater. The center of rotation ($P$) of the male skater is shown.
The man in this case acts like the centripetal Force. He exerts an inward force towards him which keeps the woman moving in a circle about him. In the non inertial reference frame of the rotating man, the woman acts like the centrifugal force exerting a force on the man, attempting to pull him away from his placement (center of rotation) towards her. The centrifugal force is a pseudo force required only in the non inertial reference frame and is the force she exerts on the man is due to her inertia (she would just go straight if there wasn't a centripetal force acting on her per Newton's first law).
For the purpose of applying the centripetal force equation $F=mv^{2}/R$ we can consider the figure skating pair to consist of a rigid body the center of mass being $M$ and the radius of the rotation is $R$ shown in the figure. The centripetal acceleration is then $v^{2}/R$.
Hope this helps.

A: Imagine any rotating object rotating about an axis For example a rod. Every point on the rod is rotating in a circular path about the axis with its own radius. The points near the end of the rod have larger radii and points closer to the axis have smaller radii.
As the rod is rotating each point on the rod has the same angular velocity. So the points near the end of the rod have a greater tangential velocity to cover the greater circumference in the same time as the closer points cover a smaller circumference. From this we can see that the centripetal force acting on the mass at these points further away from the axis is greater than the centripetal force on the mass at points closer to the axis.
• points with greater radii on rotating objects have greater tangential velocity as angular velocity of all points is constant. Therefore a greater centripetal force.
So the centripetal force is actually different at ever point along the rod.
