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A uniform disk of radius rolls without slipping with constant angular velocity ona horizontal surface (see figure below). A point P on the outer edge (rim) of the disk traverses

a path that traces out a cycloid given by the position vector: \vec{r}_{P}=r(\theta-\sin \theta) \hat{\imath}+r(1-\cos \theta) \hat{\jmath} where 's theta reference line is the vertical line shown in the figure. Compute the velocity Vp of the point P and use it to determine the speed |Vp|| of point P. Your final solution should be of the form: ||Vp| = rwf(8), where ra is the horizontal speed of the center of mass of the disk and f(theta) is a non-dimensional function of to be determined.

Fig: 1

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