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Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. [1] It is the most familiar of the theories of physics. The concepts it covers, such as mass, acceleration, and force, are commonly used and known. [2] The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of ...
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.
Rotational frequency, also known as rotational speed or rate of rotation (symbols ν, lowercase Greek nu, and also n), is the frequency of rotation of an object around an axis. Its SI unit is the reciprocal seconds (s −1 ); other common units of measurement include the hertz (Hz), cycles per second (cps), and revolutions per minute (rpm).
In physics, angular velocity (symbol ω or , the lowercase Greek letter omega), also known as the angular frequency vector, [1] is a pseudovector representation of how the angular position or orientation of an object changes with time, i.e. how quickly an object rotates (spins or revolves) around an axis of rotation and how fast the axis itself changes direction.
If they rotate at the speed of () about an axis along the rotation vector () then each unit vector ^ of the rotating coordinate system (such as ^, ȷ ^, or ^) abides by the following equation: ^ = ^ .
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
For example, if rotational speed (unit: revolution per minute or second) is used in place of angular speed (unit: radian per second), we must multiply by 2 π radians per revolution. In the following formulas, P is power, τ is torque, and ν (Greek letter nu) is rotational speed. = Showing units:
(Angular speed and angular velocity are related to the rotational speed and velocity by a factor of 2 π, the number of radians turned in a full rotation.) Tangential speed and rotational speed are related: the faster an object rotates around an axis, the larger the speed. Tangential speed is directly proportional to rotational speed at any ...