I've been studying physics recently particularly the uniform circular motion topic. I have read about an example that an object attached to a string moving in a vertical circular path is not a uniform circular motion due to the weight of the object always acting downward so the tension in the string varies at each point in the circular path and it kind of lead us to think that all vertical circular motions are non-uniform circular motions. A Ferris wheel in a carnival seems to be moving at uniform circular motion, is it really the case? or how is it possible? Is there a way to achieve a uniform vertical circular motion?
An object can move in a vertical circular path at constant speed as long as there is a mechanism for exerting a torque on the object so as to keep the kinetic energy of the object constant (if there is no torque exerted then the kinetic energy of the object varies because its potential energy varies as it moves up and down).
A Ferris wheel can move at a constant speed by exerting a torque on its cars via their rigid supports and a torque on the central hub. An object on a string cannot work in quite the same way because the string is not rigid. If you allow the string to bend slightly then it can exert a torque on the object, but I think it would be difficult to achieve a perfect circle in this way. Alternatively, you could attach tangential jets to the object to keep it moving at a constant speed.
But if the string is always straight and the only forces acting on the object are the tension in the string and its weight then the speed of the object will vary depending on its height, and the vertical circular motion is not uniform.
In the physics textbook problems, we assume that there are only two forces i.e. the tension and the weight and as you pointed out, the circular motion is not uniform.
However, A Ferris wheel in a carnival seems to be moving at uniform circular motion due to the extra work done by the extra mechanisms like electricity, etc. which are responsible for maintaining approximately a constant angular speed.
It is similar as we define electric potential with electrostatics. When we make the particle move, we do it by making it to move with constant speed even in presence of non-zero electric forces. It is ofcourse possible due to some extra but unspecified forces in which we don't have much interest.