Problem

A vertical shaft has a base B that is stationary relative to an inertial reference frame w...

A vertical shaft has a base B that is stationary relative to an inertial reference frame with vertical axis Z. Arm OA is attached to the vertical shaft and rotates about the Z axis with an angular velocity ωOA and an angular acceleration αOA. The z axis is coincident with the Z axis but is part of a reference frame that rotates with the arm OA. The x axis of the rotating reference frame coincides with the axis of the arm OA. At the instant shown, the y axis is perpendicular to the page and directed into the page. At this instant, the collar C is at a distance d from the Z axis, is sliding along OA with a constant speed υC (relative to the arm OA), and is rotating with a constant angular velocity ωC (relative to the xyz frame). Point D is attached to the collar and is at a distance ℓ from the x axis. At the instant shown, point D happens to be in the plane that is rotated by an angle ϕ from the xz plane. Compute the expression of the inertial velocity and acceleration of point D at the instant shown in terms of the parameters given, and express it relative to the rotating coordinate system.