The PhiTOP® (or FTOP®) is a physics toy designed not only to act as a spinning top but also to appeal to the eye and to the scientifically curious mind.1 It is currently made in two versions, one from solid aluminum and the other solid brass. Each top is highly polished, and is elliptical in one cross section and circular in another. Its name…

A spinning top or a spinning hard-boiled egg is fascinating to observe since both objects can remain upright for a relatively long time without falling over. If spun at sufficient speed on a horizontal surface, the spin axis rises to a vertical position and the bottom end tends to remain fixed in position on the surface. If the initial spin is…

The effect of the aerodynamic drag force on an object in flight is well known and has been described in this and other journals many times. At speeds less than about 1 m/s, the drag force on a sphere is proportional to the speed and is given by Stokes' law. At higher speeds, the drag force is proportional to the velocity squared and is…

A ball that is projected forward without spin on a horizontal surface will slide for a short distance before it starts rolling. Sliding friction acts to decrease the translation speed v and it acts to increase the rotation speed [omega]. When v = R[omega], where R is the ball radius, the ball will start rolling and the friction force drops almost…

In sports such as baseball, softball, golf, and tennis, a common objective is to hit the ball as fast or as far as possible. Another common objective is to hit the ball so that it spins as fast as possible, since the trajectory of the ball through the air is strongly affected by ball spin. In an attempt to enhance both the coefficient of…