Question 7.CE.9: Balancing a pencil Is it possible to balance the pointed tip......

Sketch and translate    The figure to the right shows a sketch of the situation.

Simplify and diagram      The forces exerted on the pencil are shown below. The tip of the pencil is the axis of rotation. When the pencil is tilted by only a small angle, the line defined by the gravitational force exerted by Earth on the pencil is not within the area of support of the pencil (which is just the pencil tip). This equilibrium is unstable. Having the center of mass above the axis of rotation leads to this instability. To make it stable, we need to lower the center of mass to below the axis of rotation. We can do it by attaching a pocketknife to the pencil, as shown below. Notice that the massive part of the knife is below the tip of the pencil and so is the center of mass of the system. Then when the pencil tilts, the torque due to the gravitational force brings it back to the equilibrium position.