Understanding Vertical Circular Motion: Exploring Centripetal Force in UCM

[Hamish Cruickshank]

I am having some difficulty in understanding vertical circular motion.

As I understand it, the only time the object (lets say an aeroplane flying in a vertical circle) is in uniform circular motion is at the top and the bottom of the circular path.

So if you want to find the net force on an object at the top of the circle it will be the centripetal force, because in UCM the net force is the centripetal force.

Is this right?

 

[learningphysics]

Generally uniform circular motion means a constant speed throughout the circle...

In the case of a ball attaches to a string going through a vertical circle... you don't have uniform circular motion... however at the top and bottom we do have dv/dt = 0 where v is the speed of the ball (careful to note, acceleration is not 0, ie: $$\frac{d\vec{v}}{dt}$$ is not 0 because direction is changing)...

This happens because the net force is centripetal at the top and bottom. The tension and gravity both act along the radius of the circle... There is no tangential component to the net force, so speed is constant at this moment... tangential force changes speed... centripetal force doesn't (centripetal force only changes direction).

However, in between the top and bottom we have a centripetal force and a tangential force. The tension acts along the radius... but gravity can be divided into 2 perpendicular components... one along the radius and one tangent to the circle... this results in a changing speed...

Centripetal vs. tangential are "components" of the net force... (don't think of them as independent forces in and of themselves... they are components of the net force which in this case is the vector sum of tension and gravity).

 

[ogb p]

Yes, you are correct in your understanding of vertical circular motion. In uniform circular motion (UCM), the object is moving at a constant speed along a circular path, but its velocity is constantly changing direction. This change in velocity is caused by a centripetal force, which is always directed towards the center of the circular path.

At the top and bottom of the circular path, the object is moving horizontally and is experiencing only the centripetal force, resulting in UCM. However, at other points along the circular path, the object is also experiencing gravitational force, which is directed downwards. This force must be balanced by the centripetal force in order for the object to continue moving in a circular path.

To find the net force on an object at any point along the circular path, you can use the equation Fnet = Fc + Fg, where Fc is the centripetal force and Fg is the gravitational force. At the top and bottom, where there is only a centripetal force, the net force will be equal to the centripetal force. But at other points, the net force will be a combination of the centripetal and gravitational forces.

I hope this helps clarify your understanding of vertical circular motion. It is a complex concept, but with practice and further study, you will develop a deeper understanding of it. Keep exploring and asking questions!