Converting units for angular motion

[24forChromium]

I think angular velocity can be measured in radians/second. I also heard that if I multiply a value of angular velocity that is in the units of Rad./sec. by a certain value of radius in meters, I will get m/s, but this is the instantaneous tangential velocity.

Is any of these right?

In addition, since torque is measured in N*m (cross product or something, don't quite get it), does this mean that angular velocity can be measured in m^2/s and not be instantaneous and tangential?
(Priority on the first paragraph)

 

[brainpushups]

I think angular velocity can be measured in radians/second

Yes. Those are the SI units of angular velocity.

I also heard that if I multiply a value of angular velocity that is in the units of Rad./sec. by a certain value of radius in meters, I will get m/s, but this is the instantaneous tangential velocity.

Yes the instantaneous speed of a particle is the product of its angular velocity (in radians per second) and its distance from the axis of rotation.

In addition, since torque is measured in N*m (cross product or something, don't quite get it), does this mean that angular velocity can be measured in m^2/s and not be instantaneous and tangential?
(Priority on the first paragraph)

No. Just based on the units that is not possible. Angular velocity must have units of [some angular measure]/[time]