Torque
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When twisting things, the rotational force we apply about the center
is called a torque (or moment, or moment of
force). Informally, we think of the torque as the tangential
applied force times the moment arm (length of the
lever arm)
as depicted in Fig.B.7. The moment arm is the distance from the applied force to the point being twisted. For example, in the case of a wrench turning a bolt,







For more general applied forces
, we may compute the
tangential component
by projecting
onto the
tangent direction. More precisely, the torque
about the
origin
applied at a point
may be defined by
where



Note that the torque vector
is orthogonal to both the lever
arm and the tangential-force direction. It thus points in the
direction of the angular velocity vector (along the axis of rotation).
The torque magnitude is










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Newton's Second Law for Rotations
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Rotational Kinetic Energy Revisited