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phy131studiof15:lectures:chapter10 [2015/09/24 21:10] mdawber [Rockets] |
phy131studiof15:lectures:chapter10 [2015/09/28 09:10] mdawber [A thin uniform plate] |
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| $\vec{x}_{CM}=\frac{1}{M}\int x\,dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,dy\,dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ | $\vec{x}_{CM}=\frac{1}{M}\int x\,dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,dy\,dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ | ||
| - | $\vec{y}_{CM}=\frac{1}{M}\int y\,dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,dy\,dx=\frac{1}{M}\frac{w}{2}\rho_{A}l^{2}l=\frac{w}{2}\hat{j}$ | + | $\vec{y}_{CM}=\frac{1}{M}\int y\,dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,dy\,dx=\frac{1}{M}\frac{1}{2}\rho_{A}w^{2}l=\frac{w}{2}\hat{j}$ |
