Raise the stick and set it down on the prop, placing the ends of the prop at the marked spots. Place the (nonbouncy) rubber ball on the tee. Now grasp the prop, and, as quickly as you can, yank it out from between the hinged stick and the base, pulling along the line of the base, in the direction of the opening. (Because there is some lateral play in the hinge, pulling in any way perpendicular to the base may cause the stick not to fall straight onto the base.) The ball lands in the plastic cup. Had the ball and the end of the stick fallen at the same rate, the ball should have struck the side of the cup as the two were falling. Thus, while the ball, in free fall, fell with the acceleration of gravity, the acceleration of the end of the stick must have exceeded the acceleration of gravity. You can repeat the demonstration with the steel ball to show that the result is the same no matter what the mass of the ball is.
This may seem counterintuitive until we consider that the hinged stick is falling in a rather specific way. Because one end of the stick is constrained by the hinge, gravity, in acting on the center of mass of the stick, is exerting a torque on it about the hinge. The stick thus swings in an arc, and while at any instant all points on the stick move with the same angular velocity (ω = dθ/dt), their linear velocity, ωr, depends on their distance from the hinge. The same is true for their acceleration. For the whole stick, the angular acceleration, α (= dω/dt = d2θ/dt2) is the same, but the linear acceleration, a, which equals αr, depends on the distance from the hinge. Both of these (ωr and αr) are for motion tangential to the arc that the stick makes as it falls. What we must find is the vertical component of the linear acceleration, and under what conditions it exceeds the acceleration of gravity (g).
To start, we recognize that the torque, τ, is Iα = -Mg(L/2) cos θ, where I is the moment of inertia of the stick, M is the mass of the stick, L is the length of the stick, and θ is the angle of the stick above the horizontal position. Treating the stick as if the hinge is centered on its end, its moment of inertia is (ML2)/3. Substituting this into the previous equation and rearranging gives α = -(3/2)(g/L) cos θ. The linear acceleration of the end of the stick, a, is αL = -(3/2)g cos θ. The vertical component of this is a cos θ, or d2y/dt2 = -(3/2)g cos2 θ.
We see that for a certain range of angles, then, the vertical component of acceleration of the end of the stick can exceed g. This happens when (3/2) g cos2 θ > g, or when cos2 θ > 2/3. This condition is met for all angles smaller than about 35 degrees. (cos-1 √(2/3) = 35.3 degrees.) (The tangential acceleration exceeds g when (3/2) g cos θ > g, or cos θ > 2/3. This happens for all angles smaller than about 48 degrees. (cos-1 (2/3) = 48.2 degrees.) For the demonstration, the reason we need the additional constraint of having the vertical component of the acceleration exceed g is that this way the ball and stick fall independently of each other from the start.)
This demonstration is sometimes referred to as as the “falling chimney demonstration,” because the phenomenon it illustrates plays a role in the breaking apart of chimneys as they fall when they are demolished. As the calculations above show, below a certain angle, the torque exerted by gravity at the center of mass about the base of the chimney causes the acceleration of the outer portion of the chimney to exceed that of gravity. The chimney itself must provide this additional acceleration, which creates stresses within the chimney. When these stresses become great enough, the chimney breaks apart.
You can also perform this demonstration with a meter stick (or other long, narrow board) and a small block or coin. Holding the stick horizontal, place the block or coin near one end. Now hold the stick at each end by allowing it to rest on one finger of each hand. If you now suddenly remove the finger near the end with the block or coin resting on it, that end falls, with the block or coin following it. Since the block or coin is in free fall, and the acceleration of the free end of the stick exceeds g, the stick falls away from the block or coin, which the class can see.