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An example is the calculation of the rotational kinetic energy of the Earth. As the Earth has a sidereal rotation period of 23.93 hours, it has an angular velocity of 7.29 × 10 −5 rad·s −1. [2] The Earth has a moment of inertia, I = 8.04 × 10 37 kg·m 2. [3] Therefore, it has a rotational kinetic energy of 2.14 × 10 29 J.
The equations of motion describe the movement of the center of mass of a body, which remains at a constant distance from the axis of rotation. In circular motion, the distance between the body and a fixed point on its surface remains the same, i.e., the body is assumed rigid.
A macroscopic body that is stationary (i.e. a reference frame has been chosen to correspond to the body's center of momentum) may have various kinds of internal energy at the molecular or atomic level, which may be regarded as kinetic energy, due to molecular translation, rotation, and vibration, electron translation and spin, and nuclear spin ...
rotational energy. Also called angular kinetic energy. The kinetic energy due to the rotation of an object, which forms part of its total kinetic energy. rotational speed. Also called speed of revolution. The number of complete rotations or revolutions a rotating body makes per unit time. Rydberg formula
The law of conservation of energy implies that in the absence of energy dissipation or applied torques, the angular kinetic energy is conserved, so =. The angular kinetic energy may be expressed in terms of the moment of inertia tensor I {\displaystyle \mathbf {I} } and the angular velocity vector ω {\displaystyle {\boldsymbol {\omega }}}
The cylinders with higher moment of inertia roll down a slope with a smaller acceleration, as more of their potential energy needs to be converted into the rotational kinetic energy. If a mechanical system is constrained to move parallel to a fixed plane, then the rotation of a body in the system occurs around an axis k ^ {\displaystyle \mathbf ...
An arbitrarily shaped rigid rotor is a rigid body of arbitrary shape with its center of mass fixed (or in uniform rectilinear motion) in field-free space R 3, so that its energy consists only of rotational kinetic energy (and possibly constant translational energy that can be ignored).
In classical mechanics, Euler's rotation equations are a vectorial quasilinear first-order ordinary differential equation describing the rotation of a rigid body, using a rotating reference frame with angular velocity ω whose axes are fixed to the body. They are named in honour of Leonhard Euler. Their general vector form is