Vertical Circular Motion


If you're dealing with vertical circular motion, at which two points are the velocities equal. For example, if you gave the points the values of the clock, would 2 and 10 have equal velocities or would 2 and 8 have equal velocities?


Assuming no friction, equal velocities will happen at equal altitudes, the 2 and 10 o'clock positions for example. Conservation of energy requires this. The two and ten positions have equal potential energy, being at equal altitudes, and since the sum of potential and kinetic energy is a constant, the kinetic energy at those positions must be equal. Kinetic energy is the mass of the circulating object times the square of its velocity. Since the mass is constant, then the velocities must be too.