Chapter 10 Center of Gravity
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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. 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.

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Balanced rock arches national park moab utah

Chapter 10 Center of Gravity

It doesn’t seem stable why doesn’t it fall?

Balanced Rock

Arches National Park

Moab, Utah


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

An object naturally spins around its:

center of mass

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

center of gravity


Balanced rock arches national park moab utah

Center of Gravity or Center of Mass

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

CM


Balanced rock arches national park moab utah

If an object is symmetrical and

uniform (made of the same material throughout)

the center of mass is just the center

CM


Balanced rock arches national park moab utah

If an object has more mass at one end,

the center of mass if shifted that way

CM

Lead

Plastic


Balanced rock arches national park moab utah

Where is the center of mass?


Balanced rock arches national park moab utah

Where is the center of mass?


Balanced rock arches national park moab utah

Where would the CM of a large pot be?


Balanced rock arches national park moab utah

Equal mass L/R & U/D

Actual CM

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)

1 kg

2 kg

Geometric center shown at line


Balanced rock arches national park moab utah

2 m * 1 kg

1 m * 2 kg

Multiply the mass times its distance from the center of mass

Actual CM

1 kg

2 kg

1 m

1 m

1 m


Balanced rock arches national park moab utah

CM

A massive sun and 3 small planets.

Where is the center of mass?

Sun


Balanced rock arches national park moab utah

Sun

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


Balanced rock arches national park moab utah

Sun

The sun actually wobbles a bit because…


Balanced rock arches national park moab utah

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

Sun


Balanced rock arches national park moab utah

Compare the center of mass after the explosion?

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


Balanced rock arches national park moab utah

What if the fragments are different sizes?


Balanced rock arches national park moab utah

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

Where is the center of mass


Balanced rock arches national park moab utah

If a puck is pushed across a frictionless table

It moves in a straight line at a constant speed


Balanced rock arches national park moab utah

A motion graph for this is…


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

But really just 2 things happen

1.) the object rotates around its CM

2.) the CM follows a parabolic path


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

The hammer does 2 things when tossed

1.) rotates around the CM

2.) the CM follows the typical path


Balanced rock arches national park moab utah

Now at the same time.


Balanced rock arches national park moab utah

A hammer thrown into the air


Balanced rock arches national park moab utah

The center of mass / center of gravity

is special for several reasons.


Balanced rock arches national park moab utah

FOR EXAMPLE:

Gravity pulls down on an entire meter stick (each atom)

Fg

BUT this would make calculations a bit tiresome


Balanced rock arches national park moab utah

FOR EXAMPLE:

Fg = mg

BUT you can PRETEND like the Force of gravity

is only pulling down on the CENTER OF MASS


Balanced rock arches national park moab utah

FN = mg

Fg = mg

When a fulcrum is placed under the CM,

It balances!!!

(the net force is zero)


Balanced rock arches national park moab utah

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

JUST BALANCE IT ON YOUR FINGER


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

So the object isn’t balanced


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

What if the mass was dropped down by a string?

What would happen to the CM?

Would it still balance?


Balanced rock arches national park moab utah

LET’s Try it


Balanced rock arches national park moab utah

As long as the CM of mass and the pivot point

Are in line with gravity, it will balance


Balanced rock arches national park moab utah

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)


Balanced rock arches national park moab utah

Why doesn’t the leaning tower of pisa fall?


Balanced rock arches national park moab utah

Would the object at the right fall over

?


Balanced rock arches national park moab utah

Would the object at the right fall over

YES

Fg

Fg

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


Balanced rock arches national park moab utah

This block can’t be tilted anymore without falling

Fg


Balanced rock arches national park moab utah

DEMO- Tilting box


Balanced rock arches national park moab utah

The CM is still under the base

Still a little sinking left before TIMBER!!!


Balanced rock arches national park moab utah

A bus MUST withstand an angle of 28o without tipping

Some can withstand 40o

28o

Center line

40o


Balanced rock arches national park moab utah

The CM must be lower for a greater tipping angle

Highest CM for 28o

Highest CM for 40o


Balanced rock arches national park moab utah

How do the manufacturers get the CM well below the

halfway mark, even with passengers on the top deck?

Highest CM for 40o


Balanced rock arches national park moab utah

Cargo in the back of truck should always be secured

OK


Balanced rock arches national park moab utah

If it isn’t secured or strapped in then…

OK

UH OH


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

physics

physics

Where is the book most stable

A system is most stable with the CM as low as possible.

There is a tendency towards this state.

Demo: rolling concrete


Balanced rock arches national park moab utah

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


Balanced rock arches national park moab utah

This is more stable for 2 reasons

#1 a lower CG

Which is more stable


Balanced rock arches national park moab utah

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

The object at left does not


Balanced rock arches national park moab utah

Unstable equilibrium

Stable equilibrium

Any movement lowers the CM

The CM must rise first


Balanced rock arches national park moab utah

physics

physics

physics

If the book is more stable here

Why does it not fall when upright?


Balanced rock arches national park moab utah

CM animation


Balanced rock arches national park moab utah

The object is forced to pivot at the fulcrum.

Any rotation causes the CM to rise

Stable equilibrium


Balanced rock arches national park moab utah

What about like this?

UNstable equilibrium


Balanced rock arches national park moab utah

What about here?

This object is in neutral equilibrium..

The CM doesn’t rise or fall as it rotates


Balanced rock arches national park moab utah

Equal mass L/R & U/D

Actual CM

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)

Geometric center shown at line


Balanced rock arches national park moab utah

Book questions

page 147

9, 12, 14, 17, 18, 19, 23, 24, 26


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