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The case of any number of forces acting on the same object is covered by considering the sum of all forces. A possible cause of this problem is that the third law is often stated in an abbreviated form: For every action there is an equal and opposite reaction, [8] without the details, namely that these forces act on two different objects ...
For example, consider a book at rest on a table. The Earth's gravity pulls down upon the book. The "reaction" to that "action" is not the support force from the table holding up the book, but the gravitational pull of the book acting on the Earth. [note 6] Newton's third law relates to a more fundamental principle, the conservation of momentum.
In physics, action is a scalar quantity that describes how the balance of kinetic versus potential energy of a physical system changes with trajectory. Action is significant because it is an input to the principle of stationary action, an approach to classical mechanics that is simpler for multiple objects. [1]
The Newtonian and action-principle forms are equivalent, and either one can solve the same problems, but selecting the appropriate form will make solutions much easier. The energy function in the action principles is not the total energy ( conserved in an isolated system ), but the Lagrangian , the difference between kinetic and potential energy.
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
For every action, there is an equal and opposite reaction. (In other words, whenever one body exerts a force F → {\displaystyle {\vec {F}}} onto a second body, (in some cases, which is standing still) the second body exerts the force − F → {\displaystyle -{\vec {F}}} back onto the first body.
The external forces: These are indicated by labelled arrows. In a fully solved problem, a force arrow is capable of indicating the direction and the line of action [notes 1] the magnitude; the point of application; a reaction, as opposed to an applied force, if a hash is present through the stem of the arrow
Important forces include the gravitational force and the Lorentz force for electromagnetism. In addition, Newton's third law can sometimes be used to deduce the forces acting on a particle: if it is known that particle A exerts a force F on another particle B, it follows that B must exert an equal and opposite reaction force, −F, on A.