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An important simplification to these force equations is obtained by introducing the resultant force and torque that acts on the rigid system. This resultant force and torque is obtained by choosing one of the particles in the system as a reference point, R , where each of the external forces are applied with the addition of an associated torque.
where p i = momentum of particle i, F ij = force on particle i by particle j, and F E = resultant external force (due to any agent not part of system). Particle i does not exert a force on itself. Torque. Torque τ is also called moment of a force, because it is the rotational analogue to force: [8]
In physics and engineering, a resultant force is the single force and associated torque obtained by combining a system of forces and torques acting on a rigid body via vector addition. The defining feature of a resultant force, or resultant force-torque, is that it has the same effect on the rigid body as the original system of forces. [ 1 ]
A single force acting at any point O′ of a rigid body can be replaced by an equal and parallel force F acting at any given point O and a couple with forces parallel to F whose moment is M = Fd, d being the separation of O and O′. Conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately ...
Newton's second law states that the rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction. Mathematically, F=ma (force = mass x acceleration). Newton's third law states that all forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.
Judicious selection of a coordinate system can make defining the vectors simpler when writing the equations of motion or statics. The x direction may be chosen to point down the ramp in an inclined plane problem, for example. In that case the friction force only has an x component, and the normal force only has a y component.
Graphical placing of the resultant force. Resultant force and torque replaces the effects of a system of forces acting on the movement of a rigid body. An interesting special case is a torque-free resultant, which can be found as follows: Vector addition is used to find the net force; Use the equation to determine the point of application with ...
When more than two forces are involved, the geometry is no longer a parallelogram, but the same principles apply to a polygon of forces. The resultant force due to the application of a number of forces can be found geometrically by drawing arrows for each force. The parallelogram of forces is a graphical manifestation of the addition of vectors.