We encourage you to interact with your colleagues here in conversations about this homework problem.

**Discussion and hints**

From the simulation results above, we see that point A travels on a cycloidal path, with the velocity vector for A being tangent to this path, as expected. In addition, the acceleration of A points inward to the path (again, expected). The angle between v and a is initially obtuse, implying that A is initially decreasing in speed. At some point, this angle because acute indicating that the speed of A begins to increase. In fact, this rate of change of speed becomes very large as A approaches the surface on which the disk rolls. Do you know why?

The velocity analysis is a straight-forward application of our rigid body kinematics equations where we write a velocity equation for each rotating member:

**v**_{A} = v_{C} + ω_{disk} x r_{A/C} =**ω**_{disk}** x r**_{A/C}

v_{A} = v_{B} + ω_{AB}** x r**_{A/B }= v_{B} * **i + ω**_{AB} x r_{A/B}

From these, you can solve for **ω**_{disk}** **and **ω**_{AB}.

Applying the same procedure to acceleration:

**a**_{A} = a_{C} + **α**_{disk}** x r**_{A/C}** - ω**_{disk}^{2}** r**_{A/C}

a_{A} = a_{B} + α_{AB }**x r**_{A/B}** - **ω_{AB}^{2 }r_{A/B}

produces too few equations for the number of unknowns. It is recommended that you also use the following equation in your acceleration solution:

**a**_{O} = a_{C} + α_{disk} x r_{O/C} - ω_{disk}^{2}** r**_{O/C}