Drehmomentgesetz

Drehmomentgesetz is a term used in physics and engineering to describe the fundamental relations between torque (Drehmoment) and rotational motion. It encompasses the laws that connect external torques to angular acceleration and angular momentum for rigid bodies.

The most common formulations are as follows. For a rigid body rotating about a fixed axis, the net torque τ about that axis relates to angular acceleration α by τ = I α, where I is the moment of inertia of the body about the chosen axis. In a more general form, the rotational analog of Newton’s second law states that the sum of external torques about a point equals the time rate of change of the body's angular momentum: ∑τ = dL/dt. For a rigid body, L = I ω, and if I is constant and rotation is about a principal axis, this reduces to ∑τ = I α.

Torque can also be computed directly from a force: τ = r × F, with magnitude |τ| = r F sin θ, and the direction given by the right-hand rule. In static situations, a body is in rotational equilibrium when ∑τ = 0 about any axis.

In non-ideal cases, such as variable moment of inertia or rotating about moving axes, L = I · ω and ∑τ = dL/dt remain valid, but the relations can involve tensors and time-dependent I. The concept is widely used in mechanical design, including gears, shafts, motors, and any system where rotational motion and forces interact.

Units are expressed in newton-meters (N·m) for torque, noting that N·m is also the unit of work, so context is important.