Change in the precession angle

In summary, the conversation discusses a 3 kg bicycle wheel rotating at 2484 rev/min and its precession angle after a 1.5 s time interval. The wheel is supported on one side and has a distance of 0.6 m from the center to the pivot point. The wheel is a hoop of radius 0.4 m, and its mass is assumed to be located at the rim. The equation for the precession angle is given, and using the values for h, R, g, and dt, the answer is found to be .211918 in radians. However, the answer should be given in degrees, so the correct answer is -12.148 degrees. The person initially made a mistake by giving
  • #1
lizzyb
168
0
Hi. I have: A 3 kg bicycle wheel rotating at a 2484 rev/min angular velocity has its shaft supported on one side, as show in the figure. When viewing from the left (from the positive x-axes), one sees that the wheel is rotating in a clockwise manner. The distance from the center of the wheel to the pivot point is 0.6 m. The wheel is a hoop of radius 0.4 m and its shaft is horizontal.

Assume all the mass of the system is located at the rim of the bicycle wheel. The acceleration of gravity is 9.8 m/s^2.

Find the change in the precession angle after a 1.5 s time interval.

In my book I have the equation:

[tex]d\phi = \frac{(M g h) dt}{L}[/tex]

so [tex] L = I \omega = M R^2 \omega[/tex]

therefore [tex]d\phi = \frac{(M g h) dt}{M R^2 \omega} = \frac{(g h) dt}{R^2 \omega}[/tex]

Now [tex]\omega = \frac{2484 "rev"}{"min"} \frac{1 "min"}{60 "sec"} \frac{2 \pi "rad"}{"rev"} = \frac{260.124 "rad"}{"sec"}[/tex]

and let [tex]h = 0.6, R = 0.4, g = 9.8, dt = 1.5[/tex]

Using these I came up with .211918 but the answer was wrong. Any ideas where I went wrong? Thank you.

[Edit]I tried -.211918 (the bicycle is rotating in a clockwise fashion) but that was wrong as well.
 
Last edited:
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  • #2
I was supposed to answer in degrees but I was putting the answer in radians. This has been a humbling learning experience, but alas, those are the ones that seem to make such a difference. Thanks everyone! :-)
 
  • #3
If by everyone, you mean yourself (since nobody actually did anything), then sure.

Nice to know you got the answer though
 
  • #4
Office_Shredder said:
If by everyone, you mean yourself (since nobody actually did anything), then sure.

Nice to know you got the answer though

Thanks! I figured no one responded because they saw I was on the right path and assumed I would figure it out . Hence, by not responding they aided my development. It's happened before! :-)
 

Related to Change in the precession angle

What is precession angle and how does it change?

The precession angle is the angle between the spin axis of a rotating object and its orbital axis. It changes due to gravitational and torque forces acting on the rotating object.

What causes a change in the precession angle?

A change in the precession angle is caused by external forces acting on a rotating object, such as gravitational pull from other objects or torque forces from internal mechanisms.

How does the change in precession angle affect the rotation of an object?

The change in precession angle can affect the rotation of an object by altering its orientation in space and changing the direction of its spin axis. This can also impact the object's stability and the way it moves through space.

Can the precession angle be controlled or manipulated?

In some cases, the precession angle can be controlled or manipulated through external forces, such as using thrusters on a spacecraft to adjust its spin. However, in most cases, the precession angle is a natural phenomenon that cannot be directly controlled.

How is the precession angle measured and tracked?

The precession angle can be measured and tracked using various methods, including using telescopes and other observational tools to monitor the movement of celestial objects, or using sensors and instrumentation on rotating objects to track their orientation and spin. Advanced mathematical models can also be used to predict and analyze changes in precession angle.

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