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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 ...
The unit of momentum is the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity is in meters per second then the momentum is in kilogram meters per second (kg⋅m/s). In cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters per ...
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.
Using Newton's second law, the force exerted by a body (particle 2) on another body (particle 1) is: =. The force exerted by particle 1 on particle 2 is: = According to Newton's third law, the force that particle 2 exerts on particle 1 is equal and opposite to the force that particle 1 exerts on particle 2: =
The gravitational force pulling down on the mass is no longer equal to the upward elastic force of the spring. In the terminology of the previous section, F 1 and F 3 are no longer equal. However, it is still true that F 1 = F 2 and F 3 = F 4, as this is required by Newton's third law.
The center of mass, in accordance with the law of conservation of momentum, remains in place. In physics , specifically classical mechanics , the three-body problem is to take the initial positions and velocities (or momenta ) of three point masses that orbit each other in space and calculate their subsequent trajectories using Newton's laws of ...
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
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".