What term measures an object's ability to cause turning, rotating, or twisting about an axis of rotation?

The term that accurately measures an object's ability to cause turning, rotating, or twisting about an axis of rotation is torque. Torque is a vector quantity that is calculated as the product of the force applied and the distance from the point of application of the force to the axis of rotation (also known as the moment arm). This relationship demonstrates how effectively a force can produce rotational motion.

While "moment" can refer to similar principles—specifically, the moment of force or moment of inertia in some contexts—it is more commonly connected to static situations rather than the dynamic implications of rotation that torque encompasses. Leverage refers to the mechanical advantage gained by using a lever, which involves torque but isn't a direct measure of rotational ability itself.

In summary, torque encapsulates the concept of rotational force and is essential in mechanics, as it directly relates to how forces create rotation about an axis, making it the correct choice for this question.