Vertical Uniform Circular Motion

When an object travels in circular motion vertically, the speed and the magnitude of the centripetal force changes (since gravity is taken into account). As shown in the figure below, the centripetal forces is different at different points on the vertical circular pathway.

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When the object is at the bottom of a circular pathway, the weight (mass times gravitational force) acts downward, while the normal/tension force acts upward towards the center. Thus the centripetal force is equal to the normal/tension force minus the weight. Shown below:

When the object is at the top of a circuar pathway, both the weight and the normal/tension force acts downward providing the centripetal force. Therefore, centripetal force is equal to the normal/tension force plus the weight. Shown below:

Note: when the object is on either side of the pathway, the centripetal force is equal to only the normal/tension force (because the weight is perpendicular to the normal/tension force and no component of the weight is pointing toward the center).

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