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# finalexamreview - Forces Moments and Accelerations of Rigid...

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Forces, Moments and Accelerations of Rigid Bodies (Planar) Key equations There is an F = ma equation, valid for a in an inertial frame at the COM, and a moment balance equation (Newton’s 2 nd law, or Newton/Euler law). For planar motion, we have G a m F = Σ (1) α G G I M = Σ (2a) α 0 I M O = Σ (2b) G P G G P a m r k I k M × + = Σ / ˆ ˆ α (2c) (2a) can always be used, (2b) is for a fixed axis of rotation O , and (2c) can always be used, but is most handy in “constrained” problems for which the moment do to a reaction force at P is eliminated. Equations (1)-(2) relate forces and moments with accelerations and angular accelerations. These equations are good when the given and desired quantities are forces, moments, accelerations and angular accelerations. Keep in mind that in curvilinear coordinates, accelerations can be directly related to speed, curvature, etc. Work/Energy Principle (Planar) Key equations The work energy principles for translation and rotation are 2 2 1 1 T U T = + (3) where + = θ Md r d F U 2 1 , and

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