Final answer:
As an object's radius increases, its moment of inertia increases, which in turn decreases the angular acceleration for a given torque, making it more resistant to changes in rotational speed.
Step-by-step explanation:
Considering the torque equation τ=r⋅F=I⋅α, where I is the moment of inertia (Mr²), it is clear that as an object's radius increases, its resistance to changes in its state of rotation also increases. In other words, the object's angular acceleration (α) decreases. However, even if the force (F) applied decreases as the radius increases, the torque produced might not be enough to overcome the increased moment of inertia, hence making it more difficult to change the rotational speed. This is because the moment of inertia depends not only on the mass of an object but also on the mass distribution relative to the rotation axis.
Torque, a concept in dynamics of rotational motion, follows a principle similar to Newton’s second law in linear motion. The effect of torque is akin to the effect of force in linear dynamics, and moment of inertia is the rotational analog of mass. Therefore, an increased radius means a higher moment of inertia, implying a greater resistance to angular acceleration for a given torque.