Center of Gravity

Definitions

• Center of gravity (c.g.) = the point located at the center of the object’s weight distribution

• Center of mass (c.m.) = the point located at the center of the object’s mass distribution

• For anything close to Earth the c.m. and c.g. are in the same place.

Examples of Center of Gravity• Below are different examples of where the center of gravity would be located (the X).• The c.g. of an object acts as if all the object’s weight is located at that position. • Note: the c.g. doesn’t have to be on the object.

Stability / Balancing

• If an object’s c.g. is over its base (the base is what is supporting it) then the object will balance.

• If an object’s c.g. in not over its base then the object will topple over.

• All things being equal, the lower the c.g. the more stable.

• All things being equal, the wider the base the more stable.

Women vs. Men

• Assuming each person has the same size base, why are women more stable then men?

• Women typically carry more weight lower on their torsos

• Men typically carry more weight higher on their torsos.

Center of Gravity Toys

• Toys like these balance very well. Where should most of the weight be located in order for the toy to be very stable?

• Most of the weight is in the bolts on the bottom. This will lower the c.g. and make sure the c.g. is always over the base.

More Center of Gravity Toys

• Weeble-wobble toys like these always stand back up because the c.g. is in the very bottom.

• If you apply a torque to it (causing it to rotate back and forth), it will always stand back up because the the c.g. will always remain over the base.

Leaning Tower of Pisa

• If the leaning tower of Pisa is not toppling over, where must the c.g. be located?

• The c.g. must be over the base.

Torque and C.G.

• If a force is applied through the c.g. then no torque will be applied and the ball will NOT rotate.

• If a force is NOT applied through the c.g. then a torque will be applied and the ball will rotate.

Carrying Heavy Objects• The guy on the right

is holding a heavy box. Notice what happened to his c.g.

• The guy on the left is holding the same box but holding his arm out.

• Why will the guy on the left be more stable?

Lean a little lean for me.

• Explain how it is possible for this tractor to drive on only 3 wheels.

Go through the following slides and figure out how this relates

to c.g.