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DISCUSSION THREAD
At first read through, the motion of the disk rolling on the translating wedge looks complicated. It turns out not be be so complicated; rather, it can be described through a straight-forward expression of the rigid body kinematics equation for the disk. If we focus our attention on the disk by itself, we know the direction of of motion for two points on the disk: point O moving in the negative y-direction with an unknown speed of vO, and since point C does not slip on the wedge, C moves in the negative x-direction with a known speed of vC = vA. This is as shown in the following figure.
From this, we can write the following vector kinematics equation for the disk:
vC = vO + ω x rC/O
Although this is a single vector equation, it is made up of two scalar equations due to its x- and y-components. These two scalar equations are in terms of two unknowns: ω and vO. For Part (a), solve these two equations.
For Part (b), you can now write the rigid body kinematics equations relating points O and B in order to find the vector velocity expression for point B:
vB = vO + ω x rB/O.