Homework H2.F - Fa22

Problem statement
Solution 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:

vA = vC + ωdisk x rA/C =ωdisk x rA/C
vA = vB + ω
AB x rA/B = vBi + ωAB x rA/B

From these, you can solve for ωdisk and ωAB.

Applying the same procedure to acceleration:

aA = aCαdisk x rA/C - ωdisk2 rA/C
aA = aB + α
AB x rA/B - ωABrA/B

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

aO = aC + αdisk x rO/C - ωdisk2 rO/C


 

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