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Torque has the dimension of force times distance, symbolically T −2 L 2 M and those fundamental dimensions are the same as that for energy or work. Official SI literature indicates newton-metre , is properly denoted N⋅m, as the unit for torque; although this is dimensionally equivalent to the joule , which is not used for torque.
Torque-free precessions are non-trivial solution for the situation where the torque on the right hand side is zero. When I is not constant in the external reference frame (i.e. the body is moving and its inertia tensor is not constantly diagonal) then I cannot be pulled through the derivative operator acting on L.
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 is the moment of couple; F is the magnitude of the force; d is the perpendicular distance (moment) between the two parallel forces
A body's moment of inertia about a particular axis depends both on the mass and its distribution relative to the axis, increasing with mass & distance from the axis. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment ...
The rightmost illustration shows a couple, two equal but opposite forces for which the amount of the net force is zero, but they produce the net torque = where is the distance between their lines of application. This is "pure" torque, since there is no resultant force.
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 ...
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When the center of mass is not coincident with the coordinate frame (that is, when c is nonzero), the translational and angular accelerations (a and α) are coupled, so that each is associated with force and torque components.