# dyn4 - Fall 2004 2.032 DYNAMICS Problem Set No. 4 Out:...

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2.032 DYNAMICS Fall 2004 Problem Set No. 4 Out : Wednesday, October 6, 2004 Due : Wednesday, October 13, 2004 at the beginning of class Problem 1 A rigid circular cylinder of radius a has a hole of radius 1 2 a cut out. Assume that the cylinder rolls without slipping on the ﬂoor. (i) Compute the kinetic energy and the potential energy of the cylinder using the generalized coordinate θ deﬁned below. (ii) By suitably approximating the kinetic and potential energy expressions in (i), deduce the frequency of small rocking oscillations of the cylinder about the equilibrium position θ = 0. (iii) Use the potential to plot trajectories qualitatively on the ( θ, ˙ θ ) phase plane. θ g a 1 Courtesy of Prof. T. Akylas. Used with permission.

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Problem 2 A billiard ball, initially at rest, is given a sharp impulse by a cue. The cue is held horizontally a distance h above the centerline. The ball leaves the cue with a speed v 0 and eventually acquires a ﬁnal speed of 9 7 v 0 . Show that h = 4 5 R , where R
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## This note was uploaded on 02/24/2012 for the course MECHANICAL 2.032 taught by Professor Georgehaller during the Fall '04 term at MIT.

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dyn4 - Fall 2004 2.032 DYNAMICS Problem Set No. 4 Out:...

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