Energy of a free-falling, pivoting thin rod

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The discussion revolves around calculating the angular speed of a free-falling, pivoting thin rod using the conservation of energy principle. The rod, with a length of 4.0 m, is released from a 40° angle above the horizontal and pivots about a frictionless pin. Participants note the need to consider both rotational and translational kinetic energy in the calculations. There is uncertainty about applying linear equations of motion due to the pivoting nature of the rod. Clarification on the correct application of these equations is requested to solve the problem effectively.
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Homework Statement


The thin uniform rod in Figure 10-59 has length 4.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle θ = 40° above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position.


Homework Equations




The Attempt at a Solution


I don't really know.
 
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There will be two kinds of kinetic energy you'll have to find and add together: rotational and translational. Recall your basic equations of linear and rotational motion.
 
I'm sorry, but the the problem is that the fact that it's pivoting causes me hesitation with the linear equations of motion. Could you (or someone) be more specific as to how I should apply these equations?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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