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In physics and mechanics, torque is the rotational analogue of linear force. [1] It is also referred to as the moment of force (also abbreviated to moment ). The symbol for torque is typically τ {\displaystyle {\boldsymbol {\tau }}} , the lowercase Greek letter tau .
Torsion of a square section bar Example of torsion mechanics. In the field of solid mechanics, torsion is the twisting of an object due to an applied torque [1] [2].Torsion could be defined as strain [3] [4] or angular deformation [5], and is measured by the angle a chosen section is rotated from its equilibrium position [6].
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 force and torque vectors that arise in applying Newton's laws to a rigid body can be assembled into a screw called a wrench. A force has a point of application and a line of action, therefore it defines the Plücker coordinates of a line in space and has zero pitch. A torque, on the other hand, is a pure moment that is not bound to a line ...
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line. Unfortunately, that ...
Use the center of mass as the reference point and define the moment of inertia relative to the center of mass , then the equation for the resultant torque simplifies to [23]: 1029 = ^. Motion in space of a rigid body, and the inertia matrix
The forces have a turning effect or moment called a torque about an axis which is normal (perpendicular) to the plane of the forces. The SI unit for the torque of the couple is newton metre. If the two forces are F and −F, then the magnitude of the torque is given by the following formula: = where