Harmonic Motion and uniform disk of mass

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SUMMARY

The discussion focuses on determining the period of simple harmonic motion for a uniform disk of mass m and radius R, pivoted a distance ℓ from its center of mass. The correct formula for the period T is derived as T = 2π√[I/(m*g*L)], where I is the moment of inertia given by I = ½m*R² + m*L². The initial attempts to express T incorrectly omitted necessary terms, leading to confusion in the calculations.

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xxphysics
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Homework Statement


A uniform disk of mass m and radius R lies in a vertical plane and is pivoted about a point a distance ℓcm from its center of mass in (Figure 1) . When given a small rotational displacement about the pivot, the disk undergoes simple harmonic motion.

Determine the period of this motion. Use the notation lcm for the distance ℓcm.
Express your answer in terms of π, acceleration due to gravity g, some or all of the variables m, R, and lcm.

Mazur1e.ch15.p58.jpg


Homework Equations


I = ½m*R² + m*L²

T = 2π*√[I/(m*g*L)]

The Attempt at a Solution



T = 2π*√[(R² + *L² )/(g)] was wrong
 
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xxphysics said:
T = 2π*√[(R² + *L² )/(g)] was wrong
That answer does not follow from your initial equations. I notice an asterisk to the left of the L. Did you omit something?
Please post your working.
 

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