The fall and bounce of pencils and other elongated objects

Abstract

If an inclined pencil is released from rest with its bottom end resting on a table, the bottom end will slide forward or backward or it will remain at rest at the start of the fall, then slide backward for a short period before sliding forward. The magnitude and direction of the displacement of the bottom end of the pencil depends on the initial angle of inclination, the coefficient of friction, and on the length and mass distribution of the pencil. The same ground reaction forces play a similar role in the fall of trees and chimneys, the bounce of a football and any other elongated object, and in activities such as walking and running. When an elongated object is thrown obliquely to the ground, the object can bounce either forward or backward depending on the angle of inclination at impact. Spherical objects bounce away from the thrower. The difference arises because the horizontal friction force is determined not only by the normal reaction force, but also by the line of action of the normal reaction force relative to the center of mass.