# Differences

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 phy131studiof15:lectures:chapter10 [2015/09/24 21:10]mdawber [Rockets] phy131studiof15:lectures:chapter10 [2015/09/28 09:10] (current)mdawber [A thin uniform plate] Both sides previous revision Previous revision 2015/09/28 09:10 mdawber [A thin uniform plate] 2015/09/24 21:10 mdawber [Rockets] 2015/09/24 21:00 mdawber [Center of mass] 2015/09/24 20:57 mdawber [10.P.005] 2015/09/24 20:55 mdawber [Momentum] 2015/07/22 09:37 mdawber [Momentum] 2015/07/22 09:33 mdawber created 2015/09/28 09:10 mdawber [A thin uniform plate] 2015/09/24 21:10 mdawber [Rockets] 2015/09/24 21:00 mdawber [Center of mass] 2015/09/24 20:57 mdawber [10.P.005] 2015/09/24 20:55 mdawber [Momentum] 2015/07/22 09:37 mdawber [Momentum] 2015/07/22 09:33 mdawber created Line 124: Line 124: $\vec{x}_{CM}=\frac{1}{M}\int x\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ $\vec{x}_{CM}=\frac{1}{M}\int x\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ - $\vec{y}_{CM}=\frac{1}{M}\int y\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,​dy\,​dx=\frac{1}{M}\frac{w}{2}\rho_{A}l^{2}l=\frac{w}{2}\hat{j}$ + $\vec{y}_{CM}=\frac{1}{M}\int y\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}w^{2}l=\frac{w}{2}\hat{j}$