Harmonic Motion and uniform disk of mass

In summary, a uniform disk of mass m and radius R, pivoted at a distance ℓcm from its center of mass, undergoes simple harmonic motion when given a small rotational displacement. The period of this motion can be determined using the equation T = 2π*√[I/(m*g*L)], where I = ½m*R² + m*L². The answer should be expressed in terms of π, acceleration due to gravity g, and some or all of the variables m, R, and lcm.
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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.
 

1. What is harmonic motion?

Harmonic motion is a type of periodic motion in which a system moves back and forth around a central equilibrium point. It is characterized by a sinusoidal or wave-like pattern.

2. What factors affect the period of harmonic motion?

The period of harmonic motion is affected by the mass and stiffness of the system, as well as the amplitude of the motion.

3. How does a uniform disk of mass behave in harmonic motion?

A uniform disk of mass will exhibit harmonic motion when it is suspended from a fixed point, with the center of mass as the equilibrium point. It will oscillate back and forth, with its period depending on the factors mentioned in the previous question.

4. What is the equation for calculating the period of a uniform disk in harmonic motion?

The period of a uniform disk in harmonic motion can be calculated using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia of the disk, m is the mass of the disk, g is the acceleration due to gravity, and d is the distance between the center of mass and the pivot point.

5. How is harmonic motion related to simple harmonic oscillation?

Harmonic motion is a type of simple harmonic oscillation, in which the restoring force acting on the system is directly proportional to the displacement from the equilibrium point. This results in a sinusoidal or wave-like motion, as seen in harmonic motion.

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