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How does torque change the rotation of an object?

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A diagram with labeled vector illustrations. Panel A shows vector addition with two green arrows A and B forming a parallelogram, and their sum C as a red diagonal. Panel B shows vector subtraction, with A and negative B forming resultant D. Panel C demonstrates vector components using angles and projections. Panel D uses the right-hand rule with thumbs to show the direction of the cross product E = A x B and its opposite, -E = B x A. — mechanics Figure 1: (A) The vector sum C = A + B = B + A. (B) The vector difference A + (−B) = A − B = D. (C, left) A cos θ is the component of A along B and (right) B cos θ is the component of B along A. (D, left) The right-hand rule used to find the direction of E = A × B and (right) the right-hand rule used to find the direction of −E = B × A.

In physics, torque is defined as the tendency of a force to rotate an object about an axis. It acts as a "twisting force" that changes an object's rotational state by altering its angular momentum.12

When a net torque is applied to a rigid body, it produces an angular acceleration ( $α$ ), which is the rate at which the object's angular velocity changes over time. This relationship is expressed by the equation:3

$τ = I α$

In this formula, $τ$ represents the torque and $I$ is the moment of inertia, which quantifies the object's resistance to rotational motion based on its mass and distribution relative to the axis.3

Essentially, torque changes rotation by overcoming an object's inertial resistance. If no external torque acts on a system, its angular momentum remains constant, a principle known as the conservation of angular momentum. When torque is applied, it causes the angular momentum to change at a rate equal to the magnitude of the torque applied.24