Applied torque, abbreviated as \( \tau_a \) (Greek symbol tau), is the twisting moment or rotational force intentionally exerted on an object by an external source. It is the torque delivered to a component, such as a shaft, bolt, gear, flywheel, or lever, to cause it to rotate or to resist an opposing torque.
Applied Torque Formula |
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\( T_a \;=\; F_a \cdot L \) (Applied Torque) \( F_a \;=\; \dfrac{ T_a }{ L } \) \( L \;=\; \dfrac{ T_a }{ F_a } \) |
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| Symbol | English | Metric |
| \( \tau_a \) (Greek symbol tau) = Applied Torque | \(lbf-ft\) | \(N-m\) |
| \( F_a \) = Applied Force | \(lbf\) | \(N\) |
| \( L \) = Moment Arm Length | \(ft\) | \(m\) |
In engineering, applied torque is treated as an external moment acting about an axis of rotation. If the applied torque exceeds the resisting torque (such as friction, load torque, or reaction torque), the object accelerates in rotation according to Newton's Second Law for rotational motion. If the applied torque exactly equals the resisting torque, the object remains in rotational equilibrium or continues rotating at constant angular velocity. Thus, applied torque is directly responsible for transmitting mechanical power through shafts, couplings, gears, belts, chains, and other rotating machine elements. Applied torque is measured as the product of the applied force and the perpendicular distance from the axis of rotation to the line of action of the force (the moment arm).
