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I have drawn two diagrams below A and B. Lets assume for both scenarios that they lie on some frictionless table.

Diagram A is simply a rigid L shaped object rotating around a fixed frictionless pivot p1 at constant angular velocity.

Diagram B's inner arm is also rotating at some constant angular velocity about pivot p1 but has a frictionless pivot p2 that connects the inner and outer arm . The outer arm would therefore start moving as shown by the dotted change in position.

If I wish to calculate the centripetal force in both scenarios, how do I identify the radius?

Do I use the position of the centre of mass of rigid object in scenario A? Do I use the instantaneous position of the centre of mass in scenario B?

This is just a general question (not any maths homework) as I just need clarification as to how one identifies the radius 'r' in the centripetal force formula.

enter image description here

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2 Answers 2

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$F_{cp} = m\omega^2r$

Where

$F_{cp} \to$ Centripetal force

$\omega \to$ Angular velocity

$r \to$ Radius

Here $r$ denotes the distance of the center of mass of the rods from the pivot $P_1$.

In the second case, if you wish to analyze the situation, we would consider the centrifugal force acting on the rod which is free to rotate. This would result in both the rods extending parallel to each other having a long rod something like this enter image description here

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  • $\begingroup$ Many thanks for your reply. I thought centrifugal force was a fictitious force? $\endgroup$
    – Dubious
    Commented Feb 2 at 2:03
  • $\begingroup$ @Dubious The centrifugal force is the pseudo force acting on the rotating body when analyzing the situation in the frame of reference of the rotation. we don't consider it when we are analyzing in ground frame. $\endgroup$ Commented Feb 2 at 8:38
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$\def \b {\mathbf}$

enter image description here The pseudo force is

$$\mathbf F_p=-m\,\left[\b\omega\times(\b\omega\times\,\b r)+ \b{\dot{\omega}}\times\,\b r+2\,(\b\omega\times \b v)\right]$$

where $~\b r~$ is the vector to the center of mass, $~\b v=\b{\dot{r}}~$ and $~\b\omega~$ is the angular velocity

in case B is $$\b r:=\b r_2=\b r_1+\b u-\b r_p\\ \b\omega=\b\omega_1+\b\omega_2$$

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  • $\begingroup$ Many thanks to both of you for assisting me. $\endgroup$
    – Dubious
    Commented Feb 2 at 21:14

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