Vertical Disk rolling (Goldstein page 15 ) [closed]

Consider a disk rolling on the horizontal xy plane constrained to move so that the plane of the disk is always vertical. The coordinates used to describe the motion might be x,y coordinates of the centre of the disk, an angle of rotation phi about the axis of the disk, and an angle theta between the axis of the disk and say, the x axis.

Can someone explain what is theta here?

• Doesn't it say at the end of the quote: an angle theta between the axis of the disk and say, the x axis.?? – Kyle Kanos May 9 '18 at 10:22
• Is it not the point of this question that the diagram is misleading? The angle theta should be in some way accounting for orientation. However, in the diagram, the way it's drawn (with a segment going from the point of contact of the disk to the x axis parallel to the to the y axis) this is not at all clear. In fact it seems that the angle is just 90 degrees. – Rudyard Jul 14 at 13:02

$\theta$ is the angle between the normal to the curve and the $x$-axis.
The disk can change direction as it rolls, parameterised by the angle $\theta$.