What Is Torque?
Torque is the rotational analogue of force: τ = r × F, where r is the lever-arm vector from the chosen axis to the point of force application. Magnitude: τ = rF sinθ. SI unit: N·m (numerically identical to joules but conceptually different).
Newton's second law for rotation: τnet = I α, with I the moment of inertia and α the angular acceleration. The sum of torques is zero in static equilibrium; this is what lets us solve see-saw problems and structural-load distributions.
Torque depends on the choice of axis, which is also a choice. The same force can produce zero torque about an axis through its line of action and large torque about an axis far away.
Recent research on this topic from arXiv
Preprints and papers indexed on arXiv.org. Links open the public abstract pages.
- Non-inertial torques and the Euler equation
Amir H. Fariborz · 2022 ·arXiv:2203.05150v1
The fundamental equation describing the rotational dynamics of a rigid body is ${\vec τ}=d{\vec L} / dt$ which is a straightforward consequence of the Newton's second law of motion and is only valid in an inertial coordinate system. While t... - In Situ Calibration of Six-Axes Force Torque Sensors using Accelerometer Measurements
Silvio Traversaro, Daniele Pucci, Francesco Nori · 2014 ·arXiv:1410.0885v2
This paper proposes techniques to calibrate six-axis force-torque sensors that can be performed in situ, i.e., without removing the sensor from the hosting system. We assume that the force-torque sensor is attached to a rigid body equipped... - Exact Analytic Solutions for the Rotation of an Axially Symmetric Rigid Body Subjected to a Constant Torque
Marcello Romano · 2012 ·arXiv:1204.3419v1
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtaine... - Analyzing the Motion of a Charged Rigid Body under the Influence of a Gyrostatic Torque
A. H. Elneklawy · 2025 ·arXiv:2503.00494v1
This research investigates the rotational dynamics of a charged axisymmetric spinning rigid body influenced by gyrostatic torque. The study also accounts for the effects of transverse and constant body-fixed torques and an electromagnetic f...