Uniform circular motion criteria and take off conditions

Question

Does constant angular velocity imply uniform circular motion?

When talking about a material point rotating and axis, if we know that it rotates it at constant angular velocity does it imply its rotation is that of a Uniform circular motion? If not what would miss to conclude that it's a UCM?

Also I know that a condition for take off is that the Normal force vanishes -> no more contact with surface. So if I am in a material point problem where the point initially has a normal force but after a certain time the Normal force vanishes I can conclude that it has taken off the surface right?

Answer 1

Q: Does const. angular velocity imply uniform circular motion.

A: No.

The distance from your moving point to axis can be changing. Imagine a massless line with one end fixed (axis) but freely rotating and a point with some mass that can move along this line. The line is rotating with constant angular velocity. The point can move along the line thus it is not UCM.

To have UCM you have to fix another variable besides angular momentum. It can be distance to axis, angular momentum, energy...