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Rotational energy or angular kinetic energy is kinetic energy due to the rotation of an object and is part of its total kinetic energy. Looking at rotational energy separately around an object's axis of rotation , the following dependence on the object's moment of inertia is observed: [ 1 ] E rotational = 1 2 I ω 2 {\displaystyle E_{\text ...
The evolution of the rotation of the disk is easily visualized in slow motion by looking at the top of the disk following an arrow drawn on the disk representing its radius. As the disk releases the initial energy given by the user and approaches a halt, its rotation about the vertical axis slows, while its contact point oscillation increases.
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
The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century. Early understandings of these ideas can be attributed to Thomas Young, who in his 1802 lecture to the Royal Society, was the first to use the term energy to refer to kinetic energy in its modern sense, instead of vis viva.
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]
Here, the function gives the mass density at each point (,,), is a vector perpendicular to the axis of rotation and extending from a point on the rotation axis to a point (,,) in the solid, and the integration is evaluated over the volume of the body . The moment of inertia of a flat surface is similar with the mass density being replaced by ...
Disk density is a capacity designation on magnetic storage, usually floppy disks. Each designation describes a set of characteristics that can affect the areal density of a disk or the efficiency of the encoded data.
Ehrenfest paradox – Circumference of a rotating disk should contract but not the radius, as radius is perpendicular to the direction of motion. The reference frame is fixed to the stationary center of the disk. Then the magnitude of the relative velocity of any point in the circumference of the disk is .