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In classical mechanics, the central-force problem is to determine the motion of a particle in a single central potential field.A central force is a force (possibly negative) that points from the particle directly towards a fixed point in space, the center, and whose magnitude only depends on the distance of the object to the center.
In special relativity, the rule that Wilczek called "Newton's Zeroth Law" breaks down: the mass of a composite object is not merely the sum of the masses of the individual pieces. [85]: 33 Newton's first law, inertial motion, remains true. A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the ...
Newton's Third Law is a result of applying symmetry to situations where forces can be attributed to the presence of different objects. The third law means that all forces are interactions between different bodies. [18] [19] and thus that there is no such thing as a unidirectional force or a force that acts on only one body.
and the cross-product is a pseudovector i.e. if r and p are reversed in direction (negative), L is not. In general I is an order-2 tensor, see above for its components. The dot · indicates tensor contraction. Force and Newton's 2nd law: Resultant force acts on a system at the center of mass, equal to the rate of change of momentum:
These fictitious forces are necessary for the formulation of correct equations of motion in a rotating reference frame [15] [16] and allow Newton's laws to be used in their normal form in such a frame (with one exception: the fictitious forces do not obey Newton's third law: they have no equal and opposite counterparts). [15]
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.
Newton’s Third Law of Motion (for every action there is an equal and opposite reaction) is also equivalent to the principle of conservation of momentum. Leibniz accepted the principle of conservation of momentum, but rejected the Cartesian version of it. [ 2 ]
Looking at the above formula for invariant mass of a system, one sees that, when a single massive object is at rest (v = 0, p = 0), there is a non-zero mass remaining: m 0 = E/c 2. The corresponding energy, which is also the total energy when a single particle is at rest, is referred to as "rest energy".