# Vertical circles

At the top of a circle, does the direction of the contact force depend on whether or not mg is > than or < than the resultant force?

So when mg is < than the resultant force, mg is acting downward but there is a greater force than this toward the centre, so to compensate for this the contact force must also be acting downward, so F=mg+R ( where R is the contact force ).

And when mg is > than the resulstant force, the contact force must be acting upward to provide the smaller centripetal force, so F= mg -R.

But at the bottom F always = R-mg.

However I am confused with vertical circles where e.g. a stone is being whirled. The formula for the top of the circle is always given as F = T + mg, where T is the tension. So T always acts downwards? I don't really understand this...thanks !

rock.freak667
Homework Helper
However I am confused with vertical circles where e.g. a stone is being whirled. The formula for the top of the circle is always given as F = T + mg, where T is the tension. So T always acts downwards? I don't really understand this...thanks !

The tension will always act towards the center of rotation while the weight will always act vertically downwards.

So at the top of the circle, the tension is acting down and the weight is acting down. The resultant force towards the center of the circle is F= T+mg.

At the bottom: The tension acts up towards the center of the circle and the weight acts down (away from the center of the circle). The resultant force towards the center of the circle is F=T-mg.

The tension will always act towards the center of rotation while the weight will always act vertically downwards.

So at the top of the circle, the tension is acting down and the weight is acting down. The resultant force towards the center of the circle is F= T+mg.

At the bottom: The tension acts up towards the center of the circle and the weight acts down (away from the center of the circle). The resultant force towards the center of the circle is F=T-mg.

yehh, but why does tension always act towards the centerr ? :)

ehild
Homework Helper
A string can only pull. If it is a rod, the tension can act in both directions.

ehild