Final answer:
The non-fundamental force 'rotational force' can be expressed by the formula t = mr²α, which is the rotational counterpart to Newton's second law (F = ma). This illustrates how torque, moment of inertia, and angular acceleration are interrelated in rotational dynamics.
Step-by-step explanation:
The question asked pertains to the concept of rotational force, which is not a fundamental force but rather an effect experienced in rotational motion. The mathematical formula that expresses the relationship between rotational force (torque) and rotational motion is t = mr²α. This formula is the rotational analog of Newton's second law for linear motion, which states F = ma (force equals mass times acceleration). In this context, torque (t) is analogous to force (F), the moment of inertia (mr²) is analogous to mass (m), and angular acceleration (α) is analogous to linear acceleration (a). The moment of inertia reflects how the distribution of mass affects an object's rotational motion, making it more challenging to change the object's rotational speed if the mass is distributed further from the axis of rotation.
To derive the relationship further, when a force F is applied perpendicularly to a point mass m at a distance r from a pivot point, the linear acceleration we obtain is a = F/m, which can be related to the angular acceleration since a = rα. Using the definition of torque (T), which is the product of force and the distance from the pivot point (T = Fr), and combining these expressions, we can find that torque is equal to the product of moment of inertia and angular acceleration, or T = mr²α. This equation is fundamental in rotational dynamics and allows us to solve problems involving torque and rotational motion. Understanding the concept of moment of inertia is crucial in predicting how much force it takes to change the rotational motion of an object.