Centripetal force

Centripetal force follows directly from our equations for centripetal acceleration that we saw in uniform circular motion:


Centripetal force causes an object to follow a circular path. That being said, it is not another type of force that you can add in the net force equation. Some specific force like FT or Ff will be the centripetal force.

If the specific force isn’t supplying enough (for example, FT<Fc), then the object will not follow the circular path: it will go off on a tangent. If the original centripetal force is now zero (e.g., the string breaks), then it will travel in a straight line. If it was too small but stays that way (e.g., car turning too fast), then it will follow a circle with a wider radius.

The centripetal force does not have to be provided by a single force. For example, when you spin a ball on a string in a vertical circle, there are two forces on the ball at all times: tension and gravity. They will always sum to Fc if the ball moves in a perfect circle. Since gravity doesn’t change, the tension force must change. At the top of the circle, |FT|=macmg, and at the bottom, |FT|=mac+mg.


A 1105 kg car is entering a level turn with a radius of 20.0 m at 21.5 m/s. If the coefficient of friction is 0.450, what is the maximum safe speed?

There is only one force acting on the car, the force of friction, and it needs to provide a centripetal force for the car to be safe:


We can substitute for friction and centripetal acceleration:


Now we can solve for speed:

v=rμg=(20.0 m)(0.450)(9.80 m/s2)=9.391 m/s.

Therefore, the maximum safe speed is 9.39 m/s.