Question #102373

A physical pendulum consists of a uniform solid disk of radius R supported in a vertical plane by a pivot located a distance d from the center of the disk. The disk is displaced a small angle and released.

a) Starting with T=2pi(I/mgd)^(1/2) , derive an expression for the period of the resulting simple harmonic motion in terms of the quantities given in the problem and, perhaps, constants (e.g., π, ⅓, g, ...).

b) Find an expression for the distance d that results in the shortest period and use that to write a formula for this shortest periodT. Write this result in terms of the quantities given in the problem and, perhaps, constants (e.g., π, ⅓, g, ...).

c) Calculate a numerical value for the shortest period if R = 2.35 cm.

a) Starting with T=2pi(I/mgd)^(1/2) , derive an expression for the period of the resulting simple harmonic motion in terms of the quantities given in the problem and, perhaps, constants (e.g., π, ⅓, g, ...).

b) Find an expression for the distance d that results in the shortest period and use that to write a formula for this shortest periodT. Write this result in terms of the quantities given in the problem and, perhaps, constants (e.g., π, ⅓, g, ...).

c) Calculate a numerical value for the shortest period if R = 2.35 cm.

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