Numerical and analytical calculations of rotational processes in perpendicular recording media are presented. The work supports recent experimental studies that suggest that the measurement of rotational magnetization processes can be used to determine the value of the anisotropy constant. An expression for the rotational magnetization for a noninteracting system is derived taking into account the dispersion of K and the easy-axis orientation. The calculations show that the experiments determine the mean value of HK, essentially independent of the angular dispersion. A numerical (Monte-Carlo based) micromagnetic model is used to study the effects of magnetostatic and exchange interactions at nonzero temperatures. It is shown that for small values of KV/kT, irreversible magnetization processes take place, which preclude the use of the rotational magnetization method to determine K values. This effect is enhanced by the presence of the magnetostatic interaction. However, the presence of exchange interactions is found to enforce coherent rotation in small fields, reducing the irreversible processes and allowing the determination of HK. Under these circumstances, it is shown that the exchange does not significantly affect the value of HK, and that a well-defined demagnetization correction of 4πM is appropriate. Finally, a comparison with experimental data gives good agreement for multilayer and granular media and shows the role of domain formation on the rotational magnetization process.