Physics
14.01.2022 06:44
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Consider a three dimensional harmonic oscillator with a nonlinear force such that

Consider a three dimensional harmonic oscillator with a nonlinear force such that the potential

a) calculate the force.
b) what is the lagrangian for this system?
c) what are the euler-lagrange equations?
d) find the effective potential.
e) what kind of orbits are possible-consider both small angular momentum and large angular momentum.
f) when they exist, find the radii of possible circular orbits as a function of the angular momentum.
g) which, if any of these orbits are stable?
h) for stable orbits, what is the frequency of small oscillations.
Show Answers
whyidkmyself
whyidkmyself
4,4(62 marks)

The final rotational kinetic energy of the rotating disk is 9.95 J

Explanation:

Given data,

mass 0.7 kg radius 10 cm rotates at the speed of 15 rev/sec

We have the formula,

Kf= 1/2 I ω f²

I=1/2 Mr²2

ωf= (0.8) ωo

substitute in the formula we get

Kf= 1/2 (1/2 MR²2) (0.8) ² ( ωo)²

=(0.16) M R²2 ωo²2

=(0.16)(0.7)(0.10)²(15[2π)] ²

Kf=9.95 J

The final rotational kinetic energy of the rotating disk is 9.95 J

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