Chapter 11 â Equilibrium and Elasticity - UCF Physics
Chapter 11 â Equilibrium and Elasticity - UCF Physics
Chapter 11 â Equilibrium and Elasticity - UCF Physics
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Proof:<br />
Each force F gi produces a torque τ i on the element<br />
of mass about the origin O, with moment arm x i .<br />
∑<br />
τ = r ⊥ F →τ<br />
i = xiFgi<br />
→τ<br />
net = τ i =<br />
i i<br />
∑<br />
x<br />
i<br />
F<br />
gi<br />
τ = x F = x ∑ F = τ<br />
cog<br />
g<br />
cog<br />
i<br />
gi<br />
net<br />
x<br />
cog<br />
→<br />
x<br />
∑<br />
i<br />
cog<br />
F<br />
gi<br />
=<br />
1<br />
=<br />
M<br />
∑<br />
i<br />
∑<br />
i<br />
x<br />
i<br />
F<br />
i<br />
gi<br />
x m<br />
i<br />
→x<br />
=<br />
x<br />
cog<br />
com<br />
∑<br />
i<br />
m g<br />
i<br />
i<br />
=<br />
∑<br />
i<br />
x m g<br />
i<br />
i<br />
i<br />
→<br />
x<br />
cog<br />
∑<br />
i<br />
m<br />
i<br />
=<br />
∑<br />
i<br />
x m<br />
i<br />
i
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