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Consequently, the acceleration is the second derivative of position, [7] often written . Position, when thought of as a displacement from an origin point, is a vector: a quantity with both magnitude and direction. [9]: 1 Velocity and acceleration are vector quantities as well. The mathematical tools of vector algebra provide the means to ...
The acceleration of a falling body in the absence of resistances to motion is dependent only on the gravitational field strength g (also called acceleration due to gravity). By Newton's Second Law the force acting on a body is given by: =.
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: F = m a . {\displaystyle \mathbf {F} =m\mathbf {a} \,.} 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 connection to Newton comes from Newton's second law of motion, which states that the force exerted on an object is directly proportional to the acceleration hence acquired by that object, thus: [5] =, where represents the mass of the object undergoing an acceleration .
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.
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]
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.