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Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
The second section establishes relationships between centripetal forces and the law of areas now known as Kepler's second law (Propositions 1–3), [22] and relates circular velocity and radius of path-curvature to radial force [23] (Proposition 4), and relationships between centripetal forces varying as the inverse-square of the distance to ...
In an inertial frame of reference (subscripted "in"), Euler's second law states that the time derivative of the angular momentum L equals the applied torque: = For point particles such that the internal forces are central forces, this may be derived using Newton's second law.
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vectors and matrices. These laws relate the motion of the center of gravity of a rigid body with the sum of forces and torques (or synonymously moments) acting on the rigid body.
Newton’s second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object: =, so the impulse J delivered by a steady force F acting for time Δ t is: J = F Δ t . {\displaystyle \mathbf {J} =\mathbf {F} \Delta t.}
Further, the current usage of "Kepler's Second Law" is something of a misnomer. Kepler had two versions, related in a qualitative sense: the "distance law" and the "area law". The "area law" is what became the Second Law in the set of three; but Kepler did himself not privilege it in that way. [11]
Second law: In an inertial reference frame , the vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration a of the object: F → = m a → {\displaystyle {\vec {F}}=m{\vec {a}}} .