Problem statementSolution video |

**DISCUSSION THREAD**

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**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**

v_{A/C}v

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

aa

_{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}