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victus00 [196]
3 years ago
10

How can I show that the sphere of radius R performs a simple harmonic movement. how can i set its reference point and make the f

ree body diagram.
I have the torque sum equation which is equal to the moment of inertia by angular acceleration

Physics
1 answer:
Marysya12 [62]3 years ago
5 0

Explanation:

Draw a free body diagram of the pendulum (the combination of the sphere and the massless rod).  There are three forces on the pendulum:

Weight force mg at the center of the sphere,

Reaction force in the x direction at the pivot,

Reaction force in the y direction at the pivot.

Sum the torques about the pivot O.

∑τ = I d²θ/dt²

mg (L sin θ) = I d²θ/dt²

For small θ, sin θ ≈ θ.

mg L θ = I d²θ/dt²

Since d²θ/dt² is directly proportional to θ, this fits the definition of simple harmonic motion.

If you wish, you can use parallel axis theorem to find the moment of inertia about O:

I = Icm + md²

I = ⅖ mr² + mL²

mg L θ = (⅖ mr² + mL²) d²θ/dt²

gL θ = (⅖ r² + L²) d²θ/dt²

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The potential energy for a certain mass moving in one dimension is given by U(x)=(2.0J/m3)x3−(15J/m2)x2+(36J/m)x−23JU(x)=(2.0J/m
Angelina_Jolie [31]

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Potential Energy for a certain mass is

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F=-(2\times 3x^2-15\times 2x+36)

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