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Relationship between force F, torque τ, linear momentum p, ... where p is the particle's linear momentum and r is the position vector from the origin. The time ...
Euler's first axiom or law (law of balance of linear momentum or balance of forces) states that in an inertial frame the time rate of change of linear momentum p of an arbitrary portion of a continuous body is equal to the total applied force F acting on that portion, and it is expressed as
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 direction.
Under a constant torque of magnitude τ, the speed of precession Ω P is inversely proportional to L, the magnitude of its angular momentum: = , where θ is the angle between the vectors Ω P and L. Thus, if the top's spin slows down (for example, due to friction), its angular momentum decreases and so the rate of precession increases.
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.
When the torque is zero, the angular momentum is constant, just as when the force is zero, the momentum is constant. [ 19 ] : 14–15 The torque can vanish even when the force is non-zero, if the body is located at the reference point ( r = 0 {\displaystyle \mathbf {r} =0} ) or if the force F {\displaystyle \mathbf {F} } and the displacement ...
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
Torque is the rotation equivalent of force in the same way that angle is the rotational equivalent for position, angular velocity for velocity, and angular momentum for momentum. As a consequence of Newton's first law of motion, there exists rotational inertia that ensures that all bodies maintain their angular momentum unless acted upon by an ...