Moment of a force :

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Moment of a force Vector Formulation
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Mo r ? F Mo is NOT F ? r Do Not start
with F or ..??!!!!! Can use, r1 ,
r2.etc Same answer!!
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M0 r ? F M0 r F sin ? F (r sin ? )
F d
important r goes from the point to F
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Principle of Transmissibility The force can
be slid along its line of action. The same
moment is obtained. Force is a sliding vector.
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i j k
M r ? F
rx ry rz


Fx Fy Fz
.
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2 D in a special can of 3 D MX 0 MY
0 MZ ? 0 gt The only component in 2-D
x y
MR ( ri x Fi ) Principle of Moments
Varignons theorem
French mathematician
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For concurrent Forces, M r x F1 r x
F2 ...... r x Fn r x (F1 F2 F3
. Fn) r x R

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Very important r is directed from the point
the moment is taken about to any point on
the line of action of F.
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Moment about an Axis
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• Scalar Analysis
• If the perpendicular distance d between the
  axis and the line of action of F is known ,
  then
• Maxis F d

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2) Vector Analysis Most of the time , d is
not known , thus vector analysis is
utilized. First, lets find the moment of the
force about any point on the axis , say p
Mp r x F
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This was discussed in the previous topic. Now
remember that r is the a position vector going
from any point on the axis to any point on the
line of action of F. Second, we can think of Mp
as any vector we can find the projection
component of Mp on that axis using the Dot
product discussed earlier.
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Maxis uaxis ? Mp scalar
Volume!! uaxis ? ( r x F )
( ux i uy j uz k) ? (Mx i My j
MZ k)
This is called mixed triple product ? And x
with three vectors u, r, F
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Or uX uY
uZ Maxis rX rY
rZ FX FY FZ
ltgt
In vector form Maxis Maxis uaxis
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