The way circular shafts twist when you apply force depends a lot on some key features:

1. Polar Moment of Inertia (J): For circular shafts, we calculate $J$ using the formula $J = \frac{\pi d^4}{32}$. Here, $d$ is the diameter of the shaft. If the diameter gets bigger, $J$ also gets a lot bigger.

2. Length (L): The amount a shaft twists ($\theta$) can be found using the formula $\theta = \frac{TL}{GJ}$. In this formula, $T$ is the torque (the twisting force), $G$ is a property of the material, and $J$ is the polar moment of inertia we mentioned earlier. If the length of the shaft ($L$) gets longer, the twisting ($\theta$) will also increase.

3. Material Properties (G): Different materials have different shear moduli ($G$), which shows how stiff they are against twisting. For example, aluminum has a shear modulus around 25 GPa, while steel is about 79 GPa. This means that steel won’t twist as much as aluminum when the same force is applied.

When you have a larger diameter ($d$) and a lower shear modulus ($G$), the shaft twists less. This helps the shaft work better when it has twisting forces acting on it.