The center of gravity does not always
lie within the object itself.
When an object is in motion, its center of
mass will follow a smooth line.
Rotational Mechanics
Center of Gravity
The point located
at the object’s
average position
of weight.
Center of Mass and Center of
Gravity
• Toss a baseball into the air, and it will follow a
smooth parabolic trajectory.
• Toss a baseball bat spinning into the air, and its
path is not smooth; its motion is wobbly, and it
seems to wobble all over the place.
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Locating the Center of Gravity
Method 1
• Balancing an object provides a simple
method of locating its center of gravity.
• The weight of an entire stick behaves as if
it were concentrated at the stick’s center of
gravity.
Locating the Center of Gravity, CG
Method Two:
If you suspend any object, its cg will be
located along a vertical line drawn from
the suspension point.
Why do pregnant women get backaches?
If the cg remains in a vertical line with the
“support base”, an object will not topple
over.
However, if the cg is out beyond the support
base, it will topple.
•
Consider the force
required to open a door.
Is it easier to open the
door by pushing/pulling
away from hinge (by the
door knob) or close to
hinge?
close to hinge
away from
hinge
Farther from
from hinge=
larger
rotational
effect!
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Torque
• Torque, τ, is the tendency of a force to
rotate an object about some axis
What if two or more different forces
act along a lever arm?
Door example:
τ = Fd
Unit: Newton x meter, Nm
– τ is the torque
– d is the lever arm
– F is the force
In the illustration below, more torque is applied in
the middle example than in the first example
because the Force is more effective when it is
perpendicular.
In the third example a piece of pipe is used to
extend the lever arm providing even more
torque.
Net Torque
• The net torque is the
sum of all the torques
Torque = Force x lever arm
produced by all the
forces
lever arm lever arm
Force = weight
Force = weight
Net Torque = Weight 1 x lever arm 1
ConcepTest
You are using a wrench
and trying to loosen a
rusty nut.
Which of the
arrangements shown is
most effective in
loosening the nut?
– Weight 2 x lever arm 2
Balanced Torque occurs when the net torque is ZERO
The torque on one side of the fulcrum = the torque on the other side
Where would the 300 N boy have to sit
relative to fulcrum for balanced
torque?
3 meters
??
List in order of
descending efficiency.
300 N
200 N
200 x 3 = 300 x ??
Answer: 2, 1 & 4, 3
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Review
• Notice how the torque is
the same for the boy as it
is for the girl.
• Even if the girl is
suspended by a rope 4
feet below where she was
the torques are still the
same!
• The lever arm is the
perpendicular distance
from the pivot point to the
line along which the force
acts.
weight
• Torque is the rotational counterpart of force.
• Force tends to change the motion of things;
• Torque tends to twist or change the state of
rotating things.
For torque, the perpendicular distance from the
axis of rotation is called the lever arm.
Torque is the product of the lever arm and the
force that tends to produce rotation:
Torque = lever arm x Force
QUESTION
• A uniform meterstick supported at the 25cm mark balances when a 2-kg rock is
suspended at the 0-cm end. What is the
mass of the meterstick?
25 cm
2 kg
25 cm
What is the location where all the weight
of the meter stick is acting?
Weight
of meter
stick
?
ANSWER
The mass of the meterstick is 2 kg.
The system is in equilibrium, so any torques
must be balanced.
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