The document discusses center of gravity and stability. It defines key terms like center of mass, center of gravity, and equilibrium. It explains that an object's center of gravity depends on the distribution of its mass, and that an object will topple if its center of gravity extends beyond its base of support. The document also distinguishes between stable, unstable, and neutral equilibrium based on how the center of gravity changes with displacement.

1. Centerof Gravity

2. The WHY’s about Center of Gravity
• Why doesn’t the leaning tower of Pisa topple
over?
• How far can it lean before it does topple over?
• Why is it impossible for us to stand with our
back and our heels against a wall and bend
over and touch or toes without toppling
forward?

3. What is center of gravity (CG)?
• Center of Mass – is the point where a
body can be balanced in a uniform
gravitational field. Point where most of
the mass is concentrated.
• The Center of Gravity is the single point
on an object where all of its weight is
assumed to be located.

4. Examples of center of mass/center of gravity

5. Locating the Center of Gravity
• The center of gravity of a uniform object is at
the midpoint, its geometric center.
Supporting that single point supports the
whole object.

6. Locating the Center of Gravity
• When the
distribution of mass
of the object is not
constant or the
object is not uniform
the center of gravity
shifts to the
direction of greater
mass.

7. Locating the Center of Gravity
• The CG of an object may be located where no
actual material exists.

8. Try this!
• Rest a meter stick on two extended
forefingers. Slowly bring your fingers
together. Note what occurs as your fingers
meet at the CG. When one finger gets ahead
of the other, weight on it increases, enough to
keep it from moving, while the other finger,
with less friction, slides and catches up. You
end up at 50 cm mark because the fingers
always meet at CG!

9. Locating the Center of Gravity
• Center of gravity of people.
– When you stand erect with your arms hanging at
your sides, your CG is within your body. It is
typically 2 to 3 cm below your navel and midway
between your from and back.
– The CG is slightly lower in women than in men
because women tend to be proportionally larger
in the pelvis and smaller in the shoulders.
– In children, the CG is slightly 5% higher because of
their proportionally larger heads and short legs.

10. • Can an object have more than one CG
• Where is the center of gravity of a donut?
• In the center of the hole!
• A rigid object has one CG. If it is non-rigid, such
as a piece of clay or putty, and is distorted into
different shapes, then its CG may change as its
shape does. Even then, it has one CG for any
give n shape.

11. Toppling
• If the CG of an object is above the area of
support, the object will remain upright. If the
CG extends outside the area of support, the
object will topple over.
• The Leaning Tower of Pisa does not topple
over because its CG does not extend beyond
its base! And so the tower has stood for
centuries.

12. Just a thought.......
• When you carry a heavy load –such as a pail o
water-with one arm, why do you tend to hold
your free arm out horizontally?
• You tend to hold your free arm outstretched
to shift the CG of your body away from the
load so your combined CG will more easily be
above the base of support.

13. Just a thought.......
• To resist being toppled, why does a wrestler
stand with feet wide apart and bent knees?
• A wide apart feet increase the support base.
Bent knees lower the CG.

14. Just a thought.......
• What is the importance of tails of an animal in
terms of toppling?
• Tail gives an animal the ability to shift its CG
and increase stability

15. Stability
measure of maintaining equilibrium: a measure
of the difficulty of displacing an object or
system from equilibrium.
Equilibrium is UNSTABLE when the CG is lowered
with displacement, STABLE when work must
be done to raise the CG and NEUTRAL when
displacement neither raises nor lowers the CG.

16. Stability
• A cone balances easily on
its base. To make it topple,
its CG must be raised. This
means the cone’s potential
energy must be increased,
which requires work. We
say an object that is
balanced so that any
displacement raises its CG
is in STABLE EQUILIBRIUM.

17. Stability
• If you position the cone so
that its CG is exactly above
its tip, the slightest
vibration or air current will
cause the cone to topple.
The CG is lowered by any
movement. We say that an
object balanced so that
any displacement lowers
its CG is in UNSTABLE
EQUILIBRIUM.

18. Stability
• When the cone is placed
on its side its CG is neither
raised nor lowered with
displacement. An object in
this configuration is in
NEUTRAL EQUILIBRIUM.

19. On Sky Scrappers
• The CG o a building is
lowered if much of the
structure is below ground
level. This is important
for tall, narrow structures.
The CG is deeply rooted
that its CG is actually
below ground level. It can
not fall over intact
because falling would not
lower its CG at all.

20. The CG of the three trucks parked on a hill are
shown by the X’s. Which truck/s will topple
over?

21. Answer the following:
1. Why is the CG of a baseball bat not at its
midpoint?
2. When are the CG and CM of an object the
same?
3. Cite an example of an object that has CG
where no physical material exists.
4. Why does the Leaning topple of Pisa not
topple?

22. Answer the following:
5. How far can an object be tipped before it
topples over?
6. Is the potential energy MORE, LESS, or
UNCHANGED when the CG of an object is
raised?
7. What accounts for the stability of the tall
narrow buildings?
8. What happens to the CG of a glass of water
when filled with ice? Rises, lowers, unchaged.

23. Answer the following:
9. Why do you spread your feet farther apart
when standing in a bumpy-riding vehicle?
10. Why can you not successfully bend over and
touch your toes when you stand with your
feet back and heels against a wall?
11. Differentiate the three kinds of equilibrium
according to stability.

24. ANSWERS
1. The bat has more mass at one end.
2. When the gravity does not change over
object.
3. Donut, boomerang, hollow ball, etc.
4. The CG is above the area of support.
5. Until the CG extends beyond area of support.
6. More
7. CG is below ground level.

25. ANSWERS
8. Rises
9. To increase the support base/ area of support
for stability.
10. CG will extend beyond support base/area of
support.
11.When object is displaced, CG lowers
(UNSTABLE), CG rises (STABLE), neither rises
nor lowers (NEUTRAL)

26. Stability and Balance
Stability: resistance to disruption of equilibrium
• Factors that affect stability:
– Mass, friction, horizontal position and height of
center of gravity with respect to the base of
support
Balance: ability to control equilibrium
• Foot position affects standing balance

27. 13-22

33. Summary
• A muscle develops tension and produces torque at the
joint that it crosses.
• Muscle and bones function as levers.
• The angle of muscle pull on a bone produces rotary and
parallel components of force
• When a body is motionless, it is in static equilibrium.
• The behavior of a body is greatly influenced by the
location of the center of gravity.
• Stability is the resistance to disruption of equilibrium