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## Torque
The concept of
r is the vector from the axis of rotation to the point on which the force is acting, and F is the vector of force. Torque is important in the design of machines such as engines.
Torque has dimensions of distance × force; the same as energy. However, the units of torque are usually stated as "newton metres" or "foot pounds" rather than joules. Of course this is not simply a coincidence - a torque of 1 Nm applied through a full revolution will require an energy of exactly 2π J — mathematically, A very useful special case, often given as the definition of torque in fields other than physics, is as follows:
- \
*τ*= moment arm × force
r and F mentioned above. The problem with this definition is that it does not give the direction of the torque, and hence it is difficult to use in three dimensional cases. Note that if the force is perpendicular to the displacement vector r, the moment arm will be equal to the distance to the centre, and torque will be a maximum. This gives rise to the approximation
*τ*= distance to centre × force
For example, if a person places a force of 9.8 N (1 kg) on a spanner which is 0.5 m long, the torque will be approximately 4.9 Nm, assuming that the person pulls the spanner in the direction best suited to turning bolts. Torque is the time-derivative of angular momentum, just as force is the time derivative of linear momentum. For multiple torques acting simultaneously:
L is angular momentum. See also proof of angular momentum.
Torque on a rigid body can be written in terms of rotational inertia I:
α is angular acceleration, a quantity usually measured in rad/s^{2}. The measurement of torque is important in automotive engineering, being concerned with the transmission of power from the drive train to the wheels of a vehicle. It is also used where the tightness of screws and bolts is crucial (see torque wrench). Torque is also the easiest way to explain mechanical advantage in just about every simple machine except the pulley.
A torque or torc is also a piece of jewellery made from intertwined metal strands. Examples have been discovered in Britain and Europe during archaeological surveys; a notable and exquisite example was found at the Sutton Hoo burial mound. | |||||

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