Dynamics - Very simple Q; Just need clarification

[kspabo]

Homework Statement

Homework Equations

Skipping this, as I just have a simple question

The Attempt at a Solution

Here is the full solution, but I just have one simple question about a simple step. On the part for disk B, they establish the equation vD = vB - vD/B. In the proceeding step, they set vD = 0. I have checked out a few other solutions online and they ALL do this, but none explain. I'm curious as to why this happens. Thanks!

 

[andrewkirk]

D is the point of contact between the large disc and the outside surface. It is specified to be stationary ('without slipping'), so its velocity vD is zero. That velocity is also equal to vB-vD/B, as the first term is the linear velocity of B, the centre of the big disc, and the second term is the linear velocity of D relative to B.

Putting those two facts together gives an equation 0 = vB - vD/B, which can then be used to work out the rest.

 

[kspabo]

Thank you andrewkirk, that makes sense.