Suppose an object moving in circular motion in the vertical plane (ie such that gravity points directly downwards) around a central point attached by a string; the object is constantly accelerating as its direction is constantly changing, therefore a resultant force is acting on it . This centripetal force acts radially inwards and is the resultant force of forces acting on the object.
However when I attempt to calculate such a scenario I end up with a force unaccounted for. Take the following diagram
My question is what happens to this the component of weight that is parallel to the objects tangential velocity (ie mgsinθ), surely this should be included when calculating resultant force and therefore centripetal force. Unless my understanding of centripetal force is wrong and resultant force is not always equal to it.
This can be extended to when the object's velocity is perpendicular to the ground and tension in the string/rope is parallel to the ground. We calculate that centripetal force = tension in string, why is it we completely ignore the weight of the object in our calculations. I know the tension is radial and the weight is tangential and so perpendicular, but why do we not carry out a vector sum to work out the centripetal force?