# Differences

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 phy131studiof15:lectures:chapter10 [2015/09/24 20:55]mdawber [Momentum] 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 Next 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 Line 24: Line 24: + ===== 10.P.011 ===== ===== Center of mass ===== ===== Center of mass ===== Line 50: Line 51: $\vec{P}=M\vec{v}_{CM}$ $\vec{P}=M\vec{v}_{CM}$ + + ===== 10.P.015 ===== + Line 120: Line 124: $\vec{x}_{CM}=\frac{1}{M}\int x\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ $\vec{x}_{CM}=\frac{1}{M}\int x\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}x\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}l^{2}w=\frac{l}{2}\hat{i}$ - $\vec{y}_{CM}=\frac{1}{M}\int y\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,​dy\,​dx=\frac{1}{M}\frac{w}{2}\rho_{A}l^{2}l=\frac{w}{2}\hat{j}$ + $\vec{y}_{CM}=\frac{1}{M}\int y\,​dm=\frac{1}{M}\int_{0}^{l}\int_{0}^{w}\rho_{A}y\,​dy\,​dx=\frac{1}{M}\frac{1}{2}\rho_{A}w^{2}l=\frac{w}{2}\hat{j}$ Line 231: Line 235: The key to rocket propulsion is that the momentum of the expelled gas is equal and opposite to the forward momentum of the rocket. This does not rely on any interaction with the external atmosphere. The key to rocket propulsion is that the momentum of the expelled gas is equal and opposite to the forward momentum of the rocket. This does not rely on any interaction with the external atmosphere. + + ===== 10.P.049 ===== + + ===== 10.P.045 ===== + +