I was given a question on a recent test that asked me the following:
A sphere is allowed to roll down a smooth inclined plane (No Friction), as it rolls down does its velocity remain constant, and does its angular velocity remain constant?
Now obviously I answered that both the velocity and angular velocity increase as the sphere rolls down the ramp, but I was marked wrong, my teacher said that the angular velocity doesn't increase and remains constant, because there isn't a torque acting on the sphere, but the velocity does increase.
Now here's my question, even if there wasn't a torque acting on the sphere, the velocity was still increasing, and since $v=r\omega$, and $r$ stays constant shouldn't increasing $v$ also increase $\omega$.