C of M / C of GC of M / C of GCM - single point where all the object’s mass can be CM - single point where all the object’s mass can be considered to be concentrated - at the center of an considered to be concentrated - at the center of an object’s object’s massmass distribution distribution

CG - single point where the force of gravity can be CG - single point where the force of gravity can be considered to act on the object - at the center of an considered to act on the object - at the center of an object’s object’s weightweight distribution distribution

CG & CM are located in the same place unless its an CG & CM are located in the same place unless its an incredibly huge object where “g” would vary over its size.incredibly huge object where “g” would vary over its size.

Purpose is to simplify otherwise complex objects like Purpose is to simplify otherwise complex objects like people, cars, motorcycles, etc, down to the single point people, cars, motorcycles, etc, down to the single point since it’s the point that can be seen to follow all the rules 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 of physics (N3Ls, Proj Motion, C of p, C of E, etc) we’ve been learning anyway!been learning anyway!

Locating CGLocating CGThere doesn’t need to be any matter at the CGThere doesn’t need to be any matter at the CG

Ex: Ex: Locating CGLocating CG

You know you’ve found it when support at that point You know you’ve found it when support at that point supports the entire object!supports the entire object! Only at geometric center if object is symmetrical and Only at geometric center if object is symmetrical and made from uniform material made from uniform material

Ex:Ex: A rotating object (or system of objects) will A rotating object (or system of objects) will wobble if its CG wobble if its CG isn’tisn’t at its geometric center at its geometric center

Ex: Ex: for 1D objects, slide trick works bestfor 1D objects, slide trick works best for 2 or 3D objects, plumb line method works bestfor 2 or 3D objects, plumb line method works best

Toppling & StabilityToppling & StabilityRule for Toppling - If the CG is above the area of support Rule for Toppling - If the CG is above the area of support (the base), it won’t topple. (the base), it won’t topple.

How to tell? Draw a plumb line… How to tell? Draw a plumb line…

Ex: Leaning tower of PisaEx: Leaning tower of Pisa

Toppling & StabilityToppling & Stability

Toppling & StabilityToppling & Stability

Street performer in New OrleansVision Club’s Mississippi Trip 2014

Toppling & StabilityToppling & StabilityWhat about the human body? Where is its CM??What about the human body? Where is its CM??

It varies from person to It varies from person to

person.person.

And within a person,And within a person,

it shifts as they change it shifts as they change

position. position.

Toppling & StabilityToppling & StabilityStability – how easy it is to topple something overStability – how easy it is to topple something over

3 States of Equilibrium – an object in a position such that a 3 States of Equilibrium – an object in a position such that a force applied to it…force applied to it…

Stable Equilibrium - …raises its CGStable Equilibrium - …raises its CG

Unstable Equilibrium – …lowers its CGUnstable Equilibrium – …lowers its CG

Neutral Equilibrium – …doesn’t alter its CGNeutral Equilibrium – …doesn’t alter its CG

Critical Tipping Angle – the angle through Critical Tipping Angle – the angle through

which an object is rotated which places which an object is rotated which places

it in unstable equilibriumit in unstable equilibrium

What makes an object more stable?What makes an object more stable?

Lower CG & Wider baseLower CG & Wider base

Ex: “Weebles wobble but they don’t fall down…”Ex: “Weebles wobble but they don’t fall down…”

Falling WaterFalling WaterHouse built in mid House built in mid

1930’s 1930’s

under the under the architectural architectural direction of direction of Frank Lloyd Frank Lloyd Wright Wright

for the Kaufmann for the Kaufmann family family

in Bear Run, PA in Bear Run, PA

SUV’s and trucks tip easilySUV’s and trucks tip easilyT Rex not a predator, but a scavenger?!?T Rex not a predator, but a scavenger?!?Ping Pong ball in with dried beans or ricePing Pong ball in with dried beans or riceDouble cone rolls up the rampDouble cone rolls up the ramp

Extreme StabilityExtreme StabilityWhat happens if the CG of the object is located below its What happens if the CG of the object is located below its point of support?point of support?

Then, any movement lifts the CG, Then, any movement lifts the CG,

but its almost impossible to get the CG to be but its almost impossible to get the CG to be unsupported by the base,unsupported by the base,

so the object is extremely stable! so the object is extremely stable!

Ex: Ex: purple bird purple bird

horse & riderhorse & rider

Seattle Space NeedleSeattle Space Needle

unicycle at UPMC Sportsworksunicycle at UPMC Sportsworks

tightrope walker in trainingtightrope walker in trainingspoon, fork, match & glassspoon, fork, match & glass

A few other applications of CM…A few other applications of CM…

The Fosbury Flop – High Jump Technique

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