What relationship does linear acceleration have with angular acceleration?

The relationship between linear acceleration $(\overrightarrow{a})$ and angular acceleration $(\overrightarrow{\alpha })$ is given by $\overrightarrow{a}=\overrightarrow{\alpha }\times \overrightarrow{r}$ .
The magnitude of the linear acceleration will increase as the angular acceleration does.
For instance, increased wheel angular acceleration indicates increased vehicle acceleration. Additionally, the car's linear acceleration will be lower for a given value of angular acceleration the smaller the car's wheels are.