# Circular motion, free-body diagram

I having difficulty in explaining to my son the free-body diagram for following problem:

A child flies a toy sphere attached at the end of a light elastic string. The string is level with the horizontal...

The actual question is easy to solve using uniform circular motion equations (and has nothing to do with my question). In the free-body diagram below, what is the balancing force in the question mark?

• What force is $F_W$? – Sanya May 6 '17 at 13:58
• @Sanya , its the weight. – Mitchell May 6 '17 at 14:50
• I'm not sure I understand where's the problem: circular motion is accelerated motion so forces don't balance... – ZeroTheHero May 6 '17 at 18:14

The force is actually not perfectly horizontal. There will be some angle $\theta$ with respect to the horizontal such that the vertical component of the tension in the string is equal to the weight of the object. The faster the object is spun, the more tension in the string, and this increases the height of the object and thus lowers the angle $\theta$.

EDIT: I was assuming this problem was more basic than to include aerodynamic lift, i.e. I assumed a vacuum. Farcher's answer is correct in the event that the string is perfectly horizontal and we can include aerodynamic effects.

• How would you explain it if the toy was replaced by a stone ? I think @blackened wants to ask about what balances the body in the horizontal plane. – Mitchell May 6 '17 at 14:57
• Right! Edited the question accordingly. – blackened May 6 '17 at 15:00
• @blackened Have you changed your question? Did I adequately address your initial question regarding the force where you have a question mark? Regarding the force balance in the horizontal plane, the force balances itself over time as it rotates. Think of adding up all the force vectors at each point in time for one full revolution. The net force will be zero. Am I addressing your question? – gdbb89 May 6 '17 at 18:45
• As I understand it, the motion I describe is impossible without aerodynamic lift. It is curious that none of the books I searched touches this point. – blackened May 6 '17 at 19:00

If the string is horizontal then ? is the lift on the airplane due to the airflow over its wings.

• So this motion is impossible on the moon? – blackened May 6 '17 at 14:18
• The string could be inclined but the propeller would not be of much use. – Farcher May 6 '17 at 14:19
• So in a vacuum the motion (perfectly horizontal) is impossible? – blackened May 6 '17 at 14:53