Gyroscope Angular Speed Calculation

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SUMMARY

The discussion focuses on calculating the angular speed of a toy gyroscope with a rotor mass of 0.150 kg and a moment of inertia of 1.20×10^-4 kg m². The gyroscope precesses at a rate of one revolution every 2.40 seconds. The correct angular speed of the rotor is determined to be approximately 221 rad/s or 2111 rev/min, contrasting with the incorrect initial calculation of 38 rad/s. The participants emphasize the importance of accurately applying the gyroscopic equations and double-checking calculations.

PREREQUISITES
  • Understanding of gyroscopic motion and equations
  • Familiarity with moment of inertia concepts
  • Basic knowledge of angular velocity and precession
  • Proficiency in using LaTeX for mathematical expressions
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  • Study the equations governing gyroscopic motion in detail
  • Learn how to derive moment of inertia for various shapes
  • Explore the relationship between angular velocity and precession
  • Practice writing physics equations in LaTeX for clarity
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Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking for examples of gyroscopic calculations.

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Homework Statement




The rotor (flywheel) of a toy gyroscope has mass 0.150 kg. Its moment of inertia about its axis is 1.20*10^- 4 kg m^2. The mass of the frame is 2.70×10−2 kg. The gyroscope is supported on a single pivot with its center of mass a horizontal distance of 4.00 cm from the pivot. The gyroscope is precessing in a horizontal plane at the rate of one revolution in 2.40 s.
Find the angular speed with which the rotor is spinning about its axis, expressed in rev/min.

Homework Equations


\omega=(weight force*radius)/(moment of interia*\Omega)



The Attempt at a Solution


\omega= (1.73*.04)/(1.20*10^-4 *4.8)= 38 rad/s
the result is wrong. i have no idea what i am doing wrong.
any help would be nice thanks =)
 
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Sure, there are 3/4 mistakes in your formula.
You need to methodically write down the basic equations of the gyro, and all your data, in a neat Latex code.

You should get 221 rad/s, or 2111revs/min, if I'm not wrong.
A typical toy gyro can spin up to 3/4000 revs/min, so it makes sense (I have one toy gyro).
 

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