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When planets spin, they generate angular momentum. This does things such as cause the planet to be slightly oval-shaped, and cause deformities [6] in the planet. Another example of angular mechanics in planetary motion is orbiting around a star. Because of the speed of the orbit, they do not go plummeting into their star.
The balance of angular momentum or Euler's second law in classical mechanics is a law of physics, stating that to alter the angular momentum of a body a torque must be applied to it. An example of use is the playground merry-go-round in the picture. To put it in rotation it must be pushed.
where M k are the components of the applied torques, I k are the principal moments of inertia and ω k are the components of the angular velocity. In the absence of applied torques, one obtains the Euler top. When the torques are due to gravity, there are special cases when the motion of the top is integrable.
The formula above indicates that the angular motion is multiplied by a factor k = 1/ √ n, so that the apsidal angle α equals 180°/ √ n. This angular scaling can be seen in the apsidal precession, i.e., in the gradual rotation of the long axis of the ellipse (Figure 3).
The angular momentum of m is proportional to the perpendicular component v ⊥ of the velocity, or equivalently, to the perpendicular distance r ⊥ from the origin. Angular momentum is a vector quantity (more precisely, a pseudovector) that represents the product of a body's rotational inertia and rotational velocity (in radians/sec) about a ...
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]
An example of the first situation is an atom whose electrons only experience the Coulomb force of its atomic nucleus. If we ignore the electron–electron interaction (and other small interactions such as spin–orbit coupling), the orbital angular momentum l of each electron commutes with the total Hamiltonian. In this model the atomic ...
A common example of a screw is the wrench associated with a force acting on a rigid body. Let P be the point of application of the force F and let P be the vector locating this point in a fixed frame. The wrench W = (F, P × F) is a screw.