Pendulum Problem and steiner' law

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The discussion focuses on calculating the period of a uniform circular disk acting as a physical pendulum and finding an alternative pivot point that yields the same period. The period is calculated using the formula T = 2π√(I/mgh), with the correct answer for part A being 0.849 seconds. For part B, participants suggest using Steiner's law to express the moment of inertia (I) through a parallel axis. The goal is to equate the period of the disk to that of a simple pendulum to determine the radial distance r. The conversation emphasizes the application of physics principles to solve the problem effectively.
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Homework Statement


A uniform circular disk whose radius R is 14.3 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period? (b) At what radial distance r < R is there a pivot point that gives the same period? (give answer in cm)

Homework Equations


T= 2pi radical ( I / mgh )

The Attempt at a Solution


Okay, I already found part A using T= 2pi radical ( I / mgh )
Any help would be greatly appreciated =]

Part A: 0.849 s <-- It's correct.
I'm just stuck on Part B.
 
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Use steiner' law to express the I through a parallel axis..
 
You can find the radial distance by equating period of the disk to that of a simple pendulum.
 
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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