Summary of Mechanics 0) The laws of mechanics apply to any collection of material or ‘body.’ This body could be the overall system of study or any part of it. In the equations below, the forces and moments are those that show on a free body diagram. Interacting bodies cause equal and opposite forces and moments on each other. Linear Momentum Balance (LMB)/Force Balance ˙ Equation of Motion Fi = L t2 t1 I) The total force on a body is equal to its rate of change of linear momentum. L Net impulse is equal to the change in momentum. When there is no. | 1W Introduction to Statics and Dynamics ORWELL LJ E 7 M F2 N2 Andy Ruina and Rudra Pratap Pre-print for Oxford University Press January 2002 Summary of Mechanics 0 The laws of mechanics apply to any collection of material or body. This body could be the overall system of study or any part of it. In the equations below the forces and moments are those that show on a free body diagram. Interacting bodies cause equal and opposite forces and moments on each other. I Linear Momentum Balance LMB Force Balance Equation of Motion EI i L The total force on a body is equal to its rate of change of linear momentum. I Impulse-momentum integrating in time t2 _ 22 Fi -dt NL ti Net impulse is equal to the change in momentum. Ia Conservation of momentum if F 0 L 0 NL L2 L1 0 When there is no net force the linear momentum does not change. Ib Statics if L is negligible E F 0 If the inertial terms are zero the net force on system is zero. Ic II Angular Momentum Balance AMB Moment Balance Equation of motion EMC h C The sum of moments is equal to the II rate of change of angular momentum. Impulse-momentum angular t2 integrating in time Jt1 C t C Conservation of angular momentum HC 0 if MC 0 A fC HC2 - HC1 0 Statics m 0 if HC is negligible C The net angular impulse is equal to Ila the change in angular momentum. If there is no net moment about point Ilb C then the angular momentum about point C does not change. If the inertial terms are zero then the IIc total moment on the system is zero. III Power Balance 1st law of thermodynamics Equation of motion Q P Ek Ep E int E for finite time Conservation of Energy if Q P 0 Statics if EK is negligible t2 t2 Q dt Pdt A E ti ti E 0 A E E2 Ei 0 Q P E P E mt Pure Mechanics if heat flow and dissipation are negligible Heat flow plus mechanical power III into a system is equal to its change in energy kinetic potential internal . The net energy flow going in is equal IIIa to the net change in energy. If no energy flows into a system IIIb
