# Centripetal force and vertical motion

In regards to an object in vertical circular motion - such as a motorcycle going around a circular track, am I correct in saying that $$F_\text{centripetal} \neq F_\text{net}$$ ? Generally in school, we have been told that $$F_\text{net}$$ points towards the centre of the circle. Although this makes sense in a horizontal circular motion scenario, when $$F_g$$ is introduced, this idea doesn't work.

$$F_\text{net}$$ should be $$F_\text{centripetal} + F_g$$ and therefore is not in the direction of the centre of the circle. Could someone please clarify $$F_\text{net}$$ and $$F_\text{centripetal}$$ in regards to vertical circular motion? I think I get it, but have always been told that $$F_\text{centripetal}=F_\text{net}$$.

Centripetal force is not a seperate force. If the speed is constant it is called uniform circular motion, in this case the net force and centripetal force are exactly the same thing.

If the body is doing a circular motion with variable speed then in this case the net force is not in the radial direction, however its radial component is exactly the centripetal force. And its tangential component is responsible for the change of speed along the circular path.

• Any force pointed towards the circle-centre is called centripetal.
• In uniform circular motion, the net force $$F_{net}$$ is towards the circle-centre.

Therefore $$F_{centripetal}=F_{net}$$ is true in uniform circular motion. Always. Both vertically and horizontally. Any force involved is included in $$F_{net}$$, also $$F_g$$. If there is a $$F_g$$, which you feel might tilt the force by pullin downwards, then remember that it is being balanced by maybe a varying normal force or friction.

Now, notice the word "uniform". This means "constant speed".

In uniform circular motion there is constant speed and thus no acceleration along the direction around the path. The net force must point perpendicular to the path, towards the centre (the centripetal direction). If it didn't, then there would be a net force component parallel to the path, which would cause acceleration.

Only in constant-speed circular motion, also called uniform circular motion, is there no such parallel acceleration and thus no parallel net force component. Only then are we sure that all of the net force points straight perpendicular towards the centre, so we can call it centripetal.

Therefor in your motorcycle example, if you keep a constant speed, then $$F_{centripetal}=F_{net}\,,$$

whereas if you accelerate or decelerate, then

$$F_{centripetal}\neq F_{net}\,.$$

• Thanks, this clears things up nicely. My confusion was that the question I was answering said there was no driving force applied by the motorcycle, and I ignorantly assumed that the speed would therefore be constant. But in fact, for the speed to be constant, the motorcycle would have to be applying some sort of driving force to actually counter gravity. Oct 27 '18 at 11:26