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1.14 EQUILIBRIUM OF A PARTICLE IN SPACE

When a particle (or a rigid body) is in space, the forces acting on the rigid body (or on the particle) may be concurrent or non-concurrent. If the forces acting are concurrent, then the equation of equilibrium are

ƩFx = 0,     ƩFy = 0      and         ƩFz = 0

i.e., the resultant force in x, y and z directions are zero.

But if forces acting are non-concurrent then the resultant force in x, y and z directions should be zero also the resultant moment about x, y and z axis should be zero. i.e.,

ƩFx = 0,     ƩFy = 0      and         ƩFz = 0

Also   ƩMxy = 0,   ƩNxz = 0    and         ƩMyz = 0

*Moment is the cross product of position vector and force vector

 M = r × F

Thus there will be six equations of equilibrium, three equations of equilibrium will be for force and three equations of equilibrium will be for moment. In vector form, these equations can be written as

ƩF = 0,     ƩM = 0