Harmonic Motion and uniform disk of mass

AI Thread Summary
A uniform disk of mass m and radius R, pivoted at a distance ℓ from its center of mass, exhibits simple harmonic motion when displaced. The period of this motion is determined using the moment of inertia equation I = ½mR² + mL². The correct formula for the period T is T = 2π√[I/(mgL)], where L is the distance from the pivot to the center of mass. Participants in the discussion highlight errors in previous attempts to derive the period, emphasizing the need for accurate notation and calculations. The conversation underscores the importance of clear mathematical representation in solving physics problems.
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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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