Angular Simple Harmonic Motion

In summary, the boss at the Cut-Rate Cuckoo Clock Company asked about the frequency change in the angular SHM of the balance wheel if its dimensions were reduced by one-third. The equation used was frequency = 1/2(pi) * square root of (torsion constant/I), and taking into account the change in mass, the correct factor for the frequency change is 3.
  • #1
morbidpotato
5
0

Homework Statement



Your boss at the Cut-Rate Cuckoo Clock Company asks you what would happen to the frequency of the angular SHM of the balance wheel if it had the same density and the same coil spring (thus the same torsion constant), but all the balance wheel dimensions were made one-third as great to save material. By what factor would the frequency change?


Homework Equations



frequency = 1/2(pi) * square root of (torsion constant/I)

The Attempt at a Solution



I tried finding the factor by setting up a second equation where frequency = 1/2(pi) * square root of (torsion constant/ m(r/3)^2 since I=mr^2 and got square root 3 but it didn't work. Is it because I'm using the wrong moment of inertia equation or is it something else? Please help and many thanks in advance.
 
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  • #2
I thought for a thin disk the I=1/2Mr^2, if you reduce the radius by a factor of three, the I shoud will be 1/9th the original, hence...
 
  • #3
You also have to take into account the mass that change. Since the balance wheel dimensions were made 1/3 the original, you should have 1/27 the original mass.
 
  • #4
thanks for the help denverdoc and enter260!
 

What is Angular Simple Harmonic Motion?

Angular Simple Harmonic Motion is a type of oscillatory motion in which an object rotates back and forth around a fixed point with a constant angular frequency. It is similar to simple harmonic motion in linear systems, but instead of linear displacement, it involves angular displacement.

What is the equation for Angular Simple Harmonic Motion?

The equation for Angular Simple Harmonic Motion is θ = θ0cos(ωt + φ), where θ is the angular displacement, θ0 is the amplitude, ω is the angular frequency, and φ is the initial phase angle.

What are some real-life examples of Angular Simple Harmonic Motion?

Some examples of Angular Simple Harmonic Motion include the motion of a pendulum, the motion of a ferris wheel, and the rotation of a fan or windmill.

What factors affect the frequency of Angular Simple Harmonic Motion?

The frequency of Angular Simple Harmonic Motion is affected by the mass of the object, the length of the rotating arm, and the strength of the restoring force. The frequency is higher for smaller masses, shorter arms, and stronger restoring forces.

How is Angular Simple Harmonic Motion different from Simple Harmonic Motion?

Angular Simple Harmonic Motion involves rotational motion around a fixed point, while Simple Harmonic Motion involves linear motion back and forth along a straight line. The equations and principles governing both types of motion are similar, but the variables and units differ due to the different forms of displacement.

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