A body is moving on the xy-plane, and is rotating around the z-axis clockwise...?

Question

A body is moving on the xy-plane, and is rotating around the z-axis clockwise. What is the direction of the angular velocity? Explain your answer.

Answer 1

The direction of angular velocity has to be in the direction of the change of angle, i.e., in the axis that records the motion clockwise with respect to the z-axis. In the convention cylindrical coordinates, given by (r, phi, z), where r^2=x^2+y^2; z=z, and phi = angle counterclockwise w/respect to x-axis, then the angular change will be given in the axis given by PHI, especially -ve phi, since the motion is clockwise.
Change in angle is given in the direction of the PHI axis.
According to pinciples of vector analysis, the time-derivative of a vector is perpendicular to the vector. Thus the direction of the angular velociity (time rate of change of angle phi) is perpendicular to phi, in the z-direction (about the axis of rotation), and the direction, by the right-hand convention rule, is in the -ve z axis.

Answer 2

+z direction. We don't know anything about its path in the xy plane, so it could be a straight line with no angular momentum.

Answer 3

It obviously depends on the position and direction of the the motion relative to the x-y axes. I'm assuming those axes are rotating as mentioned? If the body itself (not the x-y axes) is rotating, then you've already anwered your ?.........

Answer 4

Hi. Negative. The 'right hand rule' for Cartesian coordinate system.