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Newton's second law, in modern form, states that the time derivative of the momentum is the force: =. If the mass m {\displaystyle m} does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration: [ 22 ] F = m d v d t ...
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference , but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total momentum does not change.
The SI unit of impulse is the newton second (N⋅s), and the dimensionally equivalent unit of momentum is the kilogram metre per second (kg⋅m/s). The corresponding English engineering unit is the pound-second (lbf⋅s), and in the British Gravitational System, the unit is the slug-foot per second (slug⋅ft/s).
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.
Since the definition of acceleration is a = dv/dt, the second law can be written in the simplified and more familiar form: =. So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle.
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.
Equivalently, the differential form of Newton's Second Law provides an alternative definition of torque: [49] =, where is the angular momentum of the particle. Newton's Third Law of Motion requires that all objects exerting torques themselves experience equal and opposite torques, [50] and therefore also directly implies the conservation of ...
The equation of motion for a particle of constant mass m is Newton's second law of 1687, in modern vector notation =, where a is its acceleration and F the resultant force acting on it. Where the mass is varying, the equation needs to be generalised to take the time derivative of the momentum.