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**Chapter 10 Center of Gravity**

It doesn’t seem stable why doesn’t it fall? Balanced Rock Arches National Park Moab, Utah

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**When a ball is spun in the air it spins around its center **

& so does a block of wood That is to say the axis of rotation is through the center of the object A hammer behaves a little differently

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**center of mass center of gravity An object naturally spins around its:**

which is very similar to (we will use these interchangeably) center of gravity

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**Center of Gravity or Center of Mass**

This is a location of the average position of mass in an object CM

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**If an object is symmetrical and **

uniform (made of the same material throughout) the center of mass is just the center CM

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**If an object has more mass at one end, **

the center of mass if shifted that way CM Lead Plastic

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**Where is the center of mass?**

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**Where is the center of mass?**

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**Where would the CM of a large pot be?**

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**But you can’t just say that there is the same amount of mass to the left and to the right**

Where do you think this set of masses connected by a string would rotate about if swung in the air At what point would there be the same mass to the left & right (assume the string is massless) Equal mass L/R & U/D Actual CM 1 kg 2 kg Geometric center shown at line

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**Multiply the mass times its distance from the center of mass**

Actual CM 1 kg 2 kg 1 m 1 m 1 m 2 m * 1 kg 1 m * 2 kg

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**A massive sun and 3 small planets.**

Where is the center of mass? Sun CM

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**The solar system does NOT rotate around the center of the sun.**

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**The sun actually wobbles a bit because…**

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**Does the center of mass of our solar system change or is it constant?**

Sun

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**Compare the center of mass after the explosion?**

If there are no outside forces, the center of mass is the same

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**What if the fragments are different sizes?**

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**Why does a washing machine vibrate during the spin cycle sometimes but not others?**

Where is the center of mass

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**If a puck is pushed across a frictionless table**

It moves in a straight line at a constant speed

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**A motion graph for this is…**

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**If a wrench is slid across a frictionless table**

The wrench below spins about is CM And its CM moves in a straight line at a constant speed

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**If a baseball is thrown into the air it follows a parabolic path**

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**If a bat is tossed it looks a little more chaotic but….**

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**But really just 2 things happen**

1.) the object rotates around its CM 2.) the CM follows a parabolic path

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If ball is thrown into the air, it follows a parabolic path (sorry can’t control the speed any better)

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**The hammer does 2 things when tossed**

1.) rotates around the CM 2.) the CM follows the typical path

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Now at the same time.

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**A hammer thrown into the air**

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**The center of mass / center of gravity**

is special for several reasons.

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FOR EXAMPLE: Gravity pulls down on an entire meter stick (each atom) Fg BUT this would make calculations a bit tiresome

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**Fg = mg BUT you can PRETEND like the Force of gravity**

FOR EXAMPLE: Fg = mg BUT you can PRETEND like the Force of gravity is only pulling down on the CENTER OF MASS

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**FN = mg Fg = mg When a fulcrum is placed under the CM, It balances!!!**

(the net force is zero)

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**This is an easy way to find the center of mass of an object**

JUST BALANCE IT ON YOUR FINGER

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**If a weight is hung at one end, what happens to the CM**

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**So the object isn’t balanced**

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**In order to be balanced the pivot must be in line with the CM**

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**What if the mass was dropped down by a string?**

What would happen to the CM? Would it still balance?

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LET’s Try it

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**As long as the CM of mass and the pivot point**

Are in line with gravity, it will balance

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Another interesting fact about the CM, it that if an object is hung by a point with a plum bob attached. The line will ALWAYS run through the CM. A Gravity Vector drawn from the pivot point will always pass through the CM (when balanced)

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**Why doesn’t the leaning tower of pisa fall?**

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**Would the object at the right fall over**

?

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**YES Would the object at the right fall over**

Fg Fg An object will topple if a vertical line through its CG is not under the support base

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**This block can’t be tilted anymore without falling**

Fg

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DEMO- Tilting box

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**Still a little sinking left before TIMBER!!!**

The CM is still under the base

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**A bus MUST withstand an angle of 28o without tipping**

Some can withstand 40o 28o Center line 40o

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**The CM must be lower for a greater tipping angle**

Highest CM for 28o Highest CM for 40o

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**How do the manufacturers get the CM well below the**

halfway mark, even with passengers on the top deck? Highest CM for 40o

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**Cargo in the back of truck should always be secured**

OK

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**If it isn’t secured or strapped in then…**

OK UH OH

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**Activity: Place your feet on the floor in front of you chair.**

Now stand up BUT notice what you do before standing!!! Demos: balanced boards hammer paint stick

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**Where is the book most stable**

physics physics A system is most stable with the CM as low as possible. There is a tendency towards this state. Demo: rolling concrete

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**If a ping pong ball is pushed into the water in a glass what happens to the CM?**

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Which is more stable This is more stable for 2 reasons #1 a lower CG

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**The object at right must have its CM go UP before falling**

The object at left does not

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**Unstable equilibrium Stable equilibrium Any movement lowers the CM**

The CM must rise first

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**If the book is more stable here**

physics physics physics Why does it not fall when upright?

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CM animation

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**Stable equilibrium The object is forced to pivot at the fulcrum.**

Any rotation causes the CM to rise Stable equilibrium

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What about like this? UNstable equilibrium

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What about here? This object is in neutral equilibrium.. The CM doesn’t rise or fall as it rotates

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**But you can’t just say that there is the same amount of mass to the left and to the right**

Where do you think this set of masses connected by a string would rotate about if swung in the air At what point would there be the same mass to the left & right (assume the string is massless) Equal mass L/R & U/D Actual CM Geometric center shown at line

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Book questions page 147 9, 12, 14, 17, 18, 19, 23, 24, 26

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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.

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.

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