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I am being asked to find the FBFD for the ball in this diagram

enter image description here

the black weight on the horizontal rod is just there to prevent the ball from wobbling around when being rotated the arrows are meant to show the motion of everything ( both clockwise ). the vertical rod rotates and depending on how fast its rotated, the string + ball either move up or down ( i forgot to include the theta )

ive drawn something like this enter image description here

but im just not sure whether the pink arrow would be a normal centripetal force, or the tension force in the x-axis.

the problem also asks how the speed of the ball is related to its rotational period and the lengths (of the string) and radius in the figure, and how the balls acceleration is related to those quantities. i'm honestly not certain at all how to figure out this question so any help/tips towards the right direction would greatly be appreciated, thanks!

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  • $\begingroup$ Hint: FBDs display the actual forces on an object. Every force has an object (the thing the force acts upon) and an agent (the cause of the force). Two objects are required. For example, the agent of weight is the Earth. What is the agent of the "pink" force? $\endgroup$ – garyp May 8 '18 at 1:18
  • $\begingroup$ I believe the agent of the pink force would then be the tension component in the X-axis, because there's no other object applying a direct force on the ball, correct? $\endgroup$ – conejo May 8 '18 at 1:48
  • $\begingroup$ Yes, the pink force is the net (sum of tension and gravity) force on the object - just enough to make it go around in a circle. $\endgroup$ – Floris May 8 '18 at 2:05
  • $\begingroup$ But you've already accounted for tension in the black arrow. So that's not the answer. $\endgroup$ – garyp May 8 '18 at 3:12
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Every force has an object and an agent. The object in question is the ball. The agent of the tension force is the string. The object of gravity is the Earth.

Let's count the forces on the ball. There is one non-contact force, gravity. The only other contact forces we have are the electrostatic force and the magnetostatic force, and they do not apply here. So we are finished with non-contact forces.

There is one contact force, tension due to the string. The only contact between the ball and the surroundings is the contact between the string and the ball. So we are finished with contact forces.

That exhausts all possibilities. There are only two forces on the ball.

So what's the pink arrow? There is no agent to associate with the pink arrow. It is not a force.

The pink arrow represents the sum of the tension force and gravity. It is not a separate force. If you represent this resultant force on a free body diagram, you have to single it out as being the resultant. For some instructors it is not appropriate to include it on the FBD at all because it is not a real force. It is neither a tension force nor a normal force.

The term centripetal force causes confusion because it is itself is not a real force in the sense of an interaction between one object and one agent. The term centripetal force refers to the resultant force that must exist if an object is observed to be executing uniform circular motion.

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