Pyörimisvoima

Pyörimisvoima, commonly translated as torque, is the tendency of a force to rotate an object around an axis. It is the rotational analog of linear force and is central to the description of rotational motion. The magnitude of pyörimisvoima is τ = r × F, where r is the position vector from the rotation axis to the point where the force is applied, F is the force, and × denotes the cross product. The magnitude can also be written τ = r F sin(φ), with φ the angle between r and F. The direction of τ is along the rotation axis, determined by the right-hand rule; its sign indicates whether the force tends to produce clockwise or counterclockwise rotation.

The SI unit of pyörimisvoima is newton meter (N·m). Note that this is a unit of moment, not energy; torque does work when the rotation angle changes.

In rotational dynamics, pyörimisvoima relates to angular acceleration α via τ = I α, where I is the moment of inertia of the object about the axis of rotation. I depends on the mass distribution: for point masses, I = ∑ m_i r_i^2; for continuous bodies, I = ∫ r^2 dm.

The work done by torque during a rotation by angle θ is W = ∫ τ dθ; for constant τ, W = τ θ (θ in radians). In systems with varying torque or friction, effective torque determines the resulting angular acceleration and energy transfer.

Common examples include the torque produced by a wrench on a bolt, the crank torque of an engine, and the driving torque of a bicycle crank. Pyörimisvoima is a central concept in mechanical design, robotics, and physics.