Meriam, Kraige & Bolton — Plane Kinematics of Rigid Bodies: Problem 5_168

*5/168 For the slider-crank of Prob. 5/167, derive the expression for the acceleration \(a_A\) of the piston (taken positive to the right) as a function of \(\theta\) for \(\omega = \dot{\theta} = \text{constant}\). Substitute the numerical data of Sample Problem 5/15 and calculate \(a_A\) as a function of \(\theta\) for \(0 \le \theta \le 180^\circ\). Plot \(a_A\) versus \(\theta\) and find the value of \(\theta\) for which \(a_A = 0\). (By symmetry anticipate the results for \(180^\circ \le \theta \le 360^\circ\).) Note: Referenced data from Sample Problem 5/15: \(r = 100 \text{ mm} = 0.1 \text{ m}\), \(l = 250 \text{ mm} = 0.25 \text{ m}\), \(\omega = 1500 \text{ rev/min} = 50\pi \text{ rad/s} \approx 157.08 \text{ rad/s}\).