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- Jan 26, 2012

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******Today is a

**big milestone**for our POTW contest! We've been doing this for 1 year now

*without missing a single week*. We hope you all continue to enjoy these problems and also that this next year we can find more exposure for these problems so students of all levels can push themselves to apply what they already know in challenging ways.

******[HR][/HR]

This week's problem is one of the most challenging we've had for this level and it requires some knowledge of physics concepts. Thank you to MarkFL for submitting this problem for us to use!

**A cue strikes a cue ball and delivers a horizontal impulse in such a way that the ball rolls without slipping as it starts to move. At what height above the ball's center (in terms of radius of the ball) was the blow struck?**

In order to solve this you will need to know the following:

1) Moment of inertia of a solid sphere: $\displaystyle I=\frac{2}{5}MR^2$

2) Parallel-axis theorem: $\displaystyle I=I_{\text{CM}}+MD^2$

3) Net torque on the ball: $\displaystyle \sum\vec{\tau}_P=F_C(R+x)=I\alpha$.

Here is a hint that explains the situation in terms of approaching the solution:

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Remember to read the POTW submission guidelines to find out how to submit your answers!