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?