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That force is the net force. [1] When forces act upon an object, they change its acceleration. The net force is the combined effect of all the forces on the object's acceleration, as described by Newton's second law of motion. When the net force is applied at a specific point on an object, the associated torque can be calculated.
Thus, using these forces in Newton's second law we find: + + = ¨, where over dots represent derivatives with respect to time, and F is the net real force (as opposed to the fictitious forces). In terms of components, this vector equation becomes: + = ¨ ˙ = ¨ , which can be compared to the equations for the inertial frame: = ¨ ˙ = ¨ + ˙ ˙ .
A modern statement of Newton's second law is a vector equation: =, where is the momentum of the system, and is the net force. [ 17 ] : 399 If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless).
That is, at =, the net force upon the body is the zero vector, and by Newton's second law, the body will not accelerate. If the force upon the body is proportional to the displacement from the equilibrium point, and directed to the equilibrium point, then the body will perform simple harmonic motion .
The action of a force is characterized by its magnitude, by the direction of its action, and by its point of application (or point of contact). Thus, force is a vector quantity, because its effect depends on the direction as well as on the magnitude of the action. [4] Forces are classified as either contact or body forces.
A net force can be viewed as being able to counteract, or resolve, the force , so the image of the dual linear transformation is really the set of resolvable forces. The relationship between these dual linear transformations is described by the work done by a velocity vector p ′ {\displaystyle p'} under a net force f {\displaystyle f} :
Interchanging the vector field v and ∇ operator, we arrive at the cross product of a vector field with curl of a vector field: = () , where ∇ F is the Feynman subscript notation, which considers only the variation due to the vector field F (i.e., in this case, v is treated as being constant in space).
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.