Equilibrium for a Particle vs. Rigid Body
For a particle, Fi = R = 0 is a sufficient condition for equilibrium For a 3-dimensional rigid body, Fi = R = 0 is a necessary but insufficient condition for equilibrium because the forces acting on it are usuall
Equilibrium for Rigid and Deformable Bodies
Equilibrium Equations: R = Fxi + Fyj + Fzk = 0 C = Mxi + Myj + Mzk = 0 Or Fx = 0 Mx = 0
Fy = 0 My = 0
Fz = 0 Mz = 0
More about Forces
External Forces applied externally or due to reaction from supports; have eff
Kinematics Motion of a Particle
A reference frame is a coordinate system specifying the positions of points by specifying the components of the position vector r relative to the origin. Suppose P is in a motion relative to the chosen reference frame, so
Straight-Line Motion
Acceleration as a function of position (e.g., gravitational forces or forces in springs)
dv dv ds dv By chain rule = = v dt ds dt ds
Substitute and re-arrange v dv = a(s ) ds Integrating from vo at so to v at position s
dv = a(s ) dt