1. Center of gravity & Center of mass
• The center of gravity, (aka center of mass) of
an object is where all the mass of an object
can be considered to be concentrated
– It is the point at which the force due to gravity
acts through.
• The center of gravity can also be thought of as
the balancing point on an object

2. How do we find C of G?
• In regularly shaped objects where the mass of
the object is evenly distributed, it’s quite easy
to find!

3. How do we find C of G?
• In more complex objects it’s a little more difficult

4. How do we find C of G?
We can find the point at which Hang the object from several points; draw line
an object will balance straight down and find intersect

5. How do we find C of G?
1.
3.
2.

6. How do we find C of G?
• The C of G location for humans is REALLY
complicated:
– It varies based on gender and age
– It varies based on our position!

7. Center of Gravity
• C of G of women is typically 55% of their height
• C of G of men is typically 57% of their height

8. Center of Gravity
• Remains fixed as long as object does
not change shape
– Varies constantly in humans as
we move!
• Humans spend most of their time
adjusting their positions to the type
of equilibrium best suited to the
task and environment
• Demo: line of gravity must remain
within its base.
– stand up and stand on one foot – how does
your position change?
– Try doing this again, but lean against the wall
so your posture does not change.
– Lean as far forward as you can while standing

9. Center of Gravity
Fig 14.9 &
14.10

10. Center of Gravity
• Objects are much more
stable (less likely to topple)
if
– the center of gravity is
located over the base
– The center of gravity is
lower to the ground
• Think of cars: top-heavy
vehicles are much more likely
to topple than cars that are
lower to the ground
– They have a wide base

11. Center of gravity & toppling
An object is less likely to topple
if C of G is lower and centered

12. Torque
• Torque is a twisting force that is required to turn an
object about its axis of rotation
• Think of a door on its hinges…what influences its
ability to rotate on its axis?
• Distance from axis of rotation
• Magnitude of the force
• Direction of the force
• More effective if force
applied is perpendicular
to the lever arm

13. Torque!
Τ=Frsinθ
Units: Nm = N*m

14. What is Torque?
Torque is defined as the Force that is applied TANGENT to the circle and at some
lever arm distance causing rotation around a specific point.
Lever Arm Distance, r
POR – Point of Rotation
Circular Path of the handle

15. Lever Arm Distance, r
POR – Point of Rotation
Torque
TWO THINGS NEED TO BE
UNDERSTOOD:
1) The displacement from a point of
rotation is necessary. Can you
unscrew a bolt without a wrench?
Maybe but it isn't easy. That extra
distance AWAY from the point of rotation
gives you the extra leverage you need.
Circular Path of the handle
THUS we call this distance the LEVER
(EFFORT) ARM (r) .
2) The Force MUST be perpendicular to the displacement. Therefore, if the
force is at an angle, sinq is needed to meet the perpendicular requirement.

16. Torque
• When there is no net torque on an object, it remains in
equilibrium (no turning)
• When there is a net torque on an object, it will rotate about its
axis of rotation
• We usually designate:
– counterclockwise motion to be
positive
– Clockwise motion to be
negative

17. Example
A 150 kg man stands 2 m from the end of a
diving board. How much torque does he
apply at the base where the board is
attached assuming the board remains
horizontal?
  Fr sin q Torque takes the units of Force
and Displacement
  mgr,q  90 
  (150)(9.8)(2)  2940 Nm

18. Example: torque applied at an angle
• An upward force of 10 Newtons is applied at a 62 degree angle to the end of a
wrench that has a 30 cm long lever arm. Calculate the torque on the wrench.

19. Example: Rotational Equilibrium
Two masses are placed on a see saw. At what distance must the
3.0 kg mass be placed in order for the seesaw to be in equilibrium
(net torque = 0). Recall that when an object is in ROTATIONAL
EQUILIBRIUM, its net torque equals zero!
- We must designate one turning direction as
positive, and the other as negative.

20. Example: Rotational Equilibrium
Two masses are placed on a see saw. At what distance must the
3.0 kg mass be placed in order for the seesaw to be in equilibrium
(net torque = 0). Recall that when an object is in ROTATIONAL
EQUILIBRIUM, its net torque equals zero!
- We must designate one turning direction as
positive, and the other as negative.

21. Example: Finding net torque on an
object
A basketball is being pushed by two players during tip-off. One player exerts a downward force of
11 N at a distance of 7.0 cm from the axis of rotation. The second player applies an upward force
of 15 N at a perpendicular distance of 14 cm from the axis of rotation. The forces are applied on
opposite sides of the ball. Find the net torque acting on the ball.

22. In which picture is the torque the
most?