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 = 5 rad/s and an angular acceleration αOA = 1.5 rad/s2.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 sliding along OA with a constant speed υC = 3.32 m/s and is rotating with a constant angular velocity ωC = 2.3 rad/s relative to the arm OA. At the instant shown, point D happens to be in the xz plane and is at a distance ℓ = 0.05 m from the x axis and at a distance d = 0.75 m from the z axis. Compute the inertial acceleration of point D, and express it relative to the rotating reference frame.