C of M / C of G CM - single point where all the object’s mass can be considered to be concentrated - at the center of an object’s mass distribution CG - single point where the force of gravity can be considered to act on the object - at the center of an object’s weight distribution CG & CM are located in the same place unless its an incredibly huge object where “g” would vary over its size. Purpose is to simplify otherwise complex objects like people, cars, motorcycles, etc, down to the single point since it’s the point that can be seen to follow all the rules of physics (N3Ls, Proj Motion, C of p, C of E, etc) we’ve been learning anyway!

Locating CG There doesn’t need to be any matter at the CG Ex: Locating CG Locating CG You know you’ve found it when support at that point supports the entire object! You know you’ve found it when support at that point supports the entire object! Only at geometric center if object is symmetrical and made from uniform material Only at geometric center if object is symmetrical and made from uniform material Ex: Ex: A rotating object (or system of objects) will wobble if its CG isn’t at its geometric center A rotating object (or system of objects) will wobble if its CG isn’t at its geometric center Ex: Ex: for 1D objects, slide trick works best for 1D objects, slide trick works best for 2 or 3D objects, plumb line method works best for 2 or 3D objects, plumb line method works best

Toppling & Stability Rule for Toppling - If the CG is above the area of support (the base), it won’t topple. How to tell? Draw a plumb line… Ex: Leaning tower of Pisa

Toppling & Stability

Street performer in New Orleans Vision Club’s Mississippi Trip 2014

Toppling & Stability What about the human body? Where is its CM?? It varies from person to person. And within a person, it shifts as they change position.

Toppling & Stability Stability – how easy it is to topple something over 3 States of Equilibrium – an object in a position such that a force applied to it… Stable Equilibrium - …raises its CG Stable Equilibrium - …raises its CG Unstable Equilibrium – …lowers its CG Unstable Equilibrium – …lowers its CG Neutral Equilibrium – …doesn’t alter its CG Neutral Equilibrium – …doesn’t alter its CG Critical Tipping Angle – the angle through which an object is rotated which places it in unstable equilibrium

What makes an object more stable? Lower CG & Wider base Ex: “Weebles wobble but they don’t fall down…”

Falling Water House built in mid 1930’s under the architectural direction of Frank Lloyd Wright for the Kaufmann family in Bear Run, PA

SUV’s and trucks tip easily T Rex not a predator, but a scavenger?!? Ping Pong ball in with dried beans or rice Double cone rolls up the ramp

Extreme Stability What happens if the CG of the object is located below its point of support? Then, any movement lifts the CG, but its almost impossible to get the CG to be unsupported by the base, so the object is extremely stable! Ex: purple bird horse & rider Seattle Space Needle

unicycle at UPMC Sportsworks tightrope walker in training spoon, fork, match & glass

A few other applications of CM… The Fosbury Flop – High Jump Technique

A high jumpers goal is to convert as much of his initial KE running toward the bar into PE to lift his CM to a maximum height. Dick Fosbury figured out that if he bent far enough into a backbend over the bar, his CM would be outside his body, below his back, and could pass under the bar, while his body passed over it, thereby he’d get more official height out of the same PE at the level of the bar. A high jumpers goal is to convert as much of his initial KE running toward the bar into PE to lift his CM to a maximum height. Dick Fosbury figured out that if he bent far enough into a backbend over the bar, his CM would be outside his body, below his back, and could pass under the bar, while his body passed over it, thereby he’d get more official height out of the same PE at the level of the bar.