Help -Pivoting Rod about center- Me

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To determine the angular acceleration of a pivoted rod with a mass attached, the total rotational inertia must be calculated, which includes both the rod and the attached mass. The system is released from a 37° angle, and the gravitational force acting on the mass contributes to the torque about the pivot. Using the formula for angular acceleration, τ = Iα, where τ is torque and I is the total moment of inertia, allows for the calculation of angular acceleration. Additionally, to find the angular velocity when the rod is vertical, conservation of energy principles can be applied. A detailed step-by-step approach is necessary to solve for both the angular acceleration and the angular velocity accurately.
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Help! ---Pivoting Rod about center---- Please Help Me!

A uniform rod is pivoted at its center and a small weight of mass M = 4.61 kg is rigidly attached to one end. The rod has length L = 6.4 m and mass mrod = 12.1 kg. The system is released from rest at the theta = 37° angle (relative to the horizontal through the pivot point).

I NEED TO FIND The angular acceleration just after it is released and the angular velocity when the rod is vertical?

I have been working on this for the last 3 hours and I cannot get the correct answer... I would greatly appreciate a step by step explanation!

Thanks in advance!
 
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Have you considered the total rotational inertia of the rod & mass?
 
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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