Abstract: The core result of Galileo's inclined plane experiment is the proportion relation between distance and

the square of time，but the local inhomogeneity of the dip angle and friction coefficient leads to inhomogeneity of local

acceleration. In this paper，a simplified model including inhomogeneity of the dip angle and friction coefficient

is introduced. Numerical results show that this inhomogeneity not only induces random error but also leads to deviation

of the square relation between the distance and the time. It is further found that if the dip angle keeps unchanged

and the friction coefficient decreases，the ball should change from non-slip rolling to slip rolling，the deviation

degree of the square relation between the distance and the time would increase rather than decrease. This result，

although contrary to intuition，coincides with the result achieved in some corresponding researches on the history

of physics. These theoretical results are confirmed by our experiments. In order to exclude the random factors in

releasing the ball，an equipment is designed to release the ball with zero velocity. A more convenient method is also

carried out to measure the friction coefficient.

Key words: Galileo's inclined plane experiment, dip angle, friction coefficient, square relation