Vertical Circular Motion

## Question:

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?
## Answer:

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.