Problem statementSolution video |

**DISCUSSION THREAD**

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**DISCUSSION and HINTS**

For your work on this problem, it is recommended that you use an observer attached to the disk. The observer/disk has two components of rotation:

- One component of
*ω*_{0}about the*fixed*-axis.**K** - The second component of
*ω*_{disk }about the*moving*-axis.**j**

Write out the angular velocity vector **ω** in terms of the two components described above.

Take a time derivative of **ω** to get the angular acceleration **α** of the observer/disk. When taking this derivative, you will need to find the time derivative of the unit vector * j*. How do you do this? Read back over Section 3.2 of the lecture book. There you will see:

*_dot =*

**j****ω**x

*, where*

**j****ω**is the total angular velocity vector of the disk that you found above.

*Acceleration of point A
*The motion of A is quite complicated. To better understand the motion of A, consider first the view of point A by our observer who is attached to the disk - what does this observer see in terms of relative velocity and relative acceleration: (

*)*

**v**_{A/B}_{rel}and (

*)*

**a**_{A/B}_{rel}?

With this known relative motion, we can use the moving reference frame acceleration equation:

* a_{A}* =

*+ (*

**a**_{B}*)*

**a**_{A/B}_{rel}+

*x*

**α***+ 2*

**r**_{A/B}**ω**x (

*)*

**v**_{A/B}_{rel}+

**ω**x (

**ω**x

*)*

**r**_{A/B}In finding the acceleration of B, * a_{B}*, note that B moves with a constant speed on a circular path centered on point O. Use the path description to find

*.*

**a**_{B}*WARNING*: Although B moves with a constant speed, its acceleration is NOT zero.