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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.
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
The maximum angular velocity of any massive object therefore depends on the size of the object. For a given |x|, the minimum upper limit occurs when ω and x are perpendicular, so that θ = π/2 and sin θ = 1. For a rotating rigid body rotating with an angular velocity ω, the u is tangential velocity at a point x inside the object. For every ...
where is the mass of the rigid body; ¯ is the velocity of the center of mass of the rigid body, as viewed by an observer fixed in an inertial frame N; ¯ is the angular momentum of the rigid body about the center of mass, also taken in the inertial frame N; and is the angular velocity of the rigid body R relative to the inertial frame N. [3]
A diagram of angular momentum. Showing angular velocity (Scalar) and radius. In physics, angular mechanics is a field of mechanics which studies rotational movement. It studies things such as angular momentum, angular velocity, and torque. It also studies more advanced things such as Coriolis force [1] and Angular aerodynamics.
One may instead change to a coordinate frame fixed in the rotating body, in which the moment of inertia tensor is constant. Using a reference frame such as that at the center of mass, the frame's position drops out of the equations. In any rotating reference frame, the time derivative must be replaced so that the equation becomes
M represents absolute angular momentum per unit mass of the fluid parcel (in m 2 / s ), u represents Earth-relative eastward component of velocity of the fluid parcel (in m / s ), φ represents latitude (in rad), and; Ω represents angular rate of Earth's rotation (in rad / s , usually 2 π rad / 1 sidereal day ≈ ...
Because of all this, when the angular velocity vector (or the angular momentum vector) is not close to the axis of highest or lowest inertia, the body "tumbles". Most moons rotate more or less around their axis of greatest inertia (due to viscous effects), but Hyperion (a moon of Saturn), two moons of Pluto and many other small bodies of the ...