Calculating Angular Momentum and Precession of a Toy Gyroscope

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Homework Help Overview

The discussion revolves around calculating the angular momentum and precession of a toy gyroscope, which includes a disk and an axle. Participants are exploring various aspects of angular momentum, torque, and precession rates based on given parameters such as mass, radius, and spinning frequency.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between torque and angular momentum, with some suggesting that the precession rate can be derived from these quantities. There are attempts to clarify how to apply the given information from previous parts of the problem to find the precession period.

Discussion Status

The discussion is active, with participants sharing insights and suggestions on how to approach the problem. Some guidance has been offered regarding the use of equations relating torque and angular momentum, though there is no explicit consensus on the final approach to part c or part d.

Contextual Notes

Participants note that they are working under time constraints due to an upcoming exam, which adds urgency to their inquiries. There is also mention of needing to use previous answers to progress in the problem.

cuz937100
A toy gyroscope consists of a M = 2.5 kg disk with a radius of R = 2 cm mounted at the end of a light axle r = 7 cm long. The gyroscope spins at f = 47 rev/s. It is held horizontal at one end of its axle and precesses about its stand as shown.

a) What is the angular momentum of the disk about its axle?
b) What is the torque about the point of support due to the weight of the gyro?
c) How long does it take the gyroscope to precess once around?
d) If the radius of the disk and the length of the axle were both doubled (R = 4 cm, r = 14 cm), and the rate at which the disk spins were kept the same, how long would it take the disk to precess once?

I have figured out parts a and b (a.0.148,b.1.72), and I thought that part c would just be the inverse of (part b/part a)(Torque/Angular Momentum) due to the fact that angular precesion is just a frequency meaning the inverse would be the period. This did not work and I can not figure out part d without part c. Can someone please help me with this problem? There is a pic of it attached...
 

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cuz937100 said:
A toy gyroscope consists of a M = 2.5 kg disk with a radius of R = 2 cm ...
HOLY CRAP!




cuz937100 said:
... I thought that part c would just be the inverse of ... (Torque/Angular Momentum) due to the fact that angular precesion is just a frequency meaning the inverse would be the period.
It seems to be just an issue of a factor of 2π. τ/L = ANGULAR frequency of precession. Recall:

f = ω/2π

=>

T = 2π/ω

That's my suggestion.
 
Ok, I understand what you're saying, but how do I apply it to the problem. The help for the problem says

C.HELP: Use the answers from parts (a) and (b).
HELP: The precession rate is the torque divided by the component of the angular momentum that is precessing.
 
Anymore suggestions? I really need help with this one, I have an exam over this section this week...
 
Use the equation torque/(Iw). This will give you your angular velocity of precession. Now you need to take 2pi divided by your result to get it in terms of angular frequency. Glad I could help cuz
 
lol, thanks a lot masamune, i already got it though...And I got it before you did ANDREW...
 

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