Haber-Schaim) The next logical step is to analyze the behavior of a real falling chimney. almost in- variably a tall chimney, falling to the ground like the stick in the previous discussion, will break in mid-air at some characteristic height. This is well documented in several photos reproduced in the literature, such as the one which appeared on the cover of the September 1976 issue of The Physics Teacher(other photos can be found in Bundy20 and Bartlett, 21 or also on our web-page ). The causes of such breaking, the height of the rupture point and the angle at which the breaking is most likely to occur, are the most natural questions which arise The first analysis- of this problem compared the fall of the real chimney to the fall of the hinged stick, but wrongly identified the center of percussion(at about two thirds of the height)as the probable point of rupture. Reynolds s first identified the possible causes of the breaking with the shear forces and the bending moment originating within the structure of the toppling chimney. More detailed analyses were given by Bundy20 and Madsen24 (the most complete papers we found on the subject)while simplified explanations are also reported 2125, 26 It even appears in graduate student study guides,27, 28 although the chimney is shown bending the wrong way in one of these books In this paper we review the theory of the real falling chimney, outlined by Madsen, 24 iming for a complete and clear explanation of this phenomenon in Sects. II and Ill. Then in Sect. IV, we propose simple ways of using small scale models (literally toy models- made with toy blocks and bricks) to test effectively the outlined theory. More information on these toy models can also be found on our web-site, together with photos and movie clips of the experiments we have performed ROTATIONAL MOTION OF THE FALLING CHIIMNEY The rotational motion of a falling chimney under gravity is equivalent to that of the falling hinged stick of Sect. I. We can describe it as in Fig. 1, where we use polar coordinates r and 6(with er and ee as unit vectors) for the position of an arbitrary point A on the longitudinal axis of the chimney, measuring the angle 0 from the vertical direction. We treat the chimney as a uniform rigid body of mass m and height H, under the action of its weight w=mg, applied to the center of gravity(basically the center of mass -CM-of the body ), and a force F exerted by the ground on the base of the chimney, assumed to act at a single point (we neglect air resistance, or any other applied force). In plane polar coordinates W=Wrer+weee=-mg cos Ber + mg sin eee F=Fer+ (1b) The moment of inertia of the chimney can be approximated with the one for a uniform thin rod, with rotation axis perpendicular to the length and passing through one end Applying the torque equation 10= T2, for a rotation around the origin, with an external torque given by T2 =mgH sin e, we find the angular acceleration T2 3 9 HHaber-Schaim19). The next logical step is to analyze the behavior of a real falling chimney. Almost in￾variably a tall chimney, falling to the ground like the stick in the previous discussion, will break in mid-air at some characteristic height. This is well documented in several photos reproduced in the literature, such as the one which appeared on the cover of the September 1976 issue of The Physics Teacher (other photos can be found in Bundy20 and Bartlett,21 or also on our web-page5 ). The causes of such breaking, the height of the rupture point and the angle at which the breaking is most likely to occur, are the most natural questions which arise. The first analysis22 of this problem compared the fall of the real chimney to the fall of the hinged stick, but wrongly identified the center of percussion (at about two thirds of the height) as the probable point of rupture. Reynolds23 first identified the possible causes of the breaking with the shear forces and the bending moment originating within the structure of the toppling chimney. More detailed analyses were given by Bundy20 and Madsen24 (the most complete papers we found on the subject) while simplified explanations are also reported.21,25,26 It even appears in graduate student study guides,27,28 although the chimney is shown bending the wrong way in one of these books. In this paper we review the theory of the real falling chimney, outlined by Madsen,24 aiming for a complete and clear explanation of this phenomenon in Sects. II and III. Then, in Sect. IV, we propose simple ways of using small scale models (literally toy models - made with toy blocks and bricks) to test effectively the outlined theory. More information on these toy models can also be found on our web-site,5 together with photos and movie clips of the experiments we have performed. II. ROTATIONAL MOTION OF THE FALLING CHIMNEY The rotational motion of a falling chimney under gravity is equivalent to that of the falling hinged stick of Sect. I. We can describe it as in Fig. 1, where we use polar coordinates r and θ (with ebr and beθ as unit vectors) for the position of an arbitrary point A on the longitudinal axis of the chimney, measuring the angle θ from the vertical direction. We treat the chimney as a uniform rigid body of mass m and height H, under the action of its weight W = mg, applied to the center of gravity (basically the center of mass -CM- of the body), and a force F exerted by the ground on the base of the chimney, assumed to act at a single point (we neglect air resistance, or any other applied force). In plane polar coordinates: W = Wrebr + Wθbeθ = −mg cos θber + mg sin θbeθ (1a) F = Frebr + Fθbeθ. (1b) The moment of inertia of the chimney can be approximated with the one for a uniform thin rod, with rotation axis perpendicular to the length and passing through one end:35 I = 1 3 mH2 . (2) Applying the torque equation I .. θ = τz, for a rotation around the origin, with an external torque given by τz = mg H 2 sin θ, we find the angular acceleration .. θ = τz I = 3 2 g H sin θ. (3) 3