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Physics 150/215 Lesson 7
Static Equilibrium
• enter of Mass
C
•Types of Motion
•Torque
•Types of Equilibrium
•Static
•Translational - Rotational
Conditions for Equilibrium
•Center of Gravity
•Free Body Diagrams
Center of Mass
=
Average position of the
masses
For example:
6 kg at x=5m & 7 kg at x=10m
x coordinate of center of mass
=
6  5  7 10 100

 7.69
6  7
13
Think of the average height of 6 monsters
that are 5m high and 7 that are 10 m high
Motion of an object can
be analyzed into three
types
t•ranslation of the center
of mass
•rotation (rigid) about
the center of mass
•vibration (elastic) about
center of mass
Translational Acceleration is
caused by the total force on the
object
If the total force FTot= 0
then there is no
Translational Acceleration
(acceleration of center of mass)
acm = 0
•Thus vcm = constant
I•f velocity of center of
mass is initially zero it
will stay zero
• here may be rotation
T
or vibrational motion
around center of mass
Rotational acceleration is
caused by the
total turning force = TORQUE
about the center of mass.
Tangential Force
Radial Force
Force
r
Force (F)
Fsin 

r
Torque 
Tangential Force   radius
 = FSinr
 FrSin  Fd
d  rSin Moment / Lever Arm
• inear = Translational
L
•Angular = Rotational
Total Force = 0; Total Torque not zero
Total Force not 0; Total Torque = 0
If the total torque Tot= 0
then there is no
Rotational Acceleration
(change of angular speed)
angular
acceleration
= 0
•Thus angular speed  = constant
I•f angular speed is initially zero
•it will stay zero
If object is RIGID
There will be no
vibration about center
of mass
Static Equilibrium for rigid
objects
vcm =
 =
FTot =
Tot =
0
0
0
0
Conditions for Static
Equilibrium for Rigid Objects
The center of mass of an object will not accelerate
if the total force on the object is zero if
Ftot   a cm  0  TRANSLATIONAL
EQUILIBRIUM
An object will have zero angular acceleration if the
total torque on the object is zero if
   0
 ROTATIONAL
EQUILIBRIUM
If the initial velocity of the center of mass is zero
and the initial angular velocity is zero they will
remain zero if
Ftot  and acm  0
When this is so the object is said to be in
STATIC EQUILIBRIUM
Properties of
Torque
The torque of a force about any point on
the line of action of that force is zero
.
If a body is in translational equilibrium and
the net torque is zero with respect to one point
in the body then it is zero with respect to all
.
points in the body
F tot  0

0
 =  0
forces
Center of Gravity
The position where the force of gravity
acts on the object or rigidly connected
objects
Free Body Diagrams
F1
N1
W1
W2
F2
N2