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In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. . It is a vector quantity, possessing a magnitude and a directi
This has the advantage that kinetic momentum can be measured experimentally whereas canonical momentum cannot. Notice that the Hamiltonian ( total energy ) can be viewed as the sum of the relativistic energy (kinetic+rest) , E = γ m c 2 {\displaystyle E=\gamma mc^{2}} , plus the potential energy , V = q φ {\displaystyle V=q\varphi
He measured momentum by the product of velocity and weight; mass is a later concept, developed by Huygens and Newton. In the swinging of a simple pendulum, Galileo says in Discourses [5] that "every momentum acquired in the descent along an arc is equal to that which causes the same moving body to ascend through the same arc." His analysis on ...
In modern notation, the momentum of a body is the product of its mass and its velocity: =, where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force: F = d p d t . {\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}\,.}
Then, the velocity of object A relative to object B is defined as the difference of the two velocity vectors: = Similarly, the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is: = Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.
The units and nature of each generalized momentum will depend on the corresponding coordinate; in this case p z is a translational momentum in the z direction, p s is also a translational momentum along the curve s is measured, and p φ is an angular momentum in the plane the angle φ is measured in. However complicated the motion of the system ...
Mathematically, if the velocity of the first object in the previous discussion is denoted by the vector u = ud and the velocity of the second object by the vector v = ve, where u is the speed of the first object, v is the speed of the second object, and d and e are unit vectors in the directions of motion of each object respectively, then the ...
Angular velocity: the angular velocity ω is the rate at which the angular position θ changes with respect to time t: = The angular velocity is represented in Figure 1 by a vector Ω pointing along the axis of rotation with magnitude ω and sense determined by the direction of rotation as given by the right-hand rule.