Gyroscopic precession

  • Thread starter cucumber
  • Start date
  • Tags
    Precession
In summary, the cucumber is desperately trying to understand physics and finds it challenging. He comes with a basic understanding of linear motion, angular velocity, and angular momentum, but is unsure about a couple of details. He asks for help from the cookiemonster, who points him in the right direction. However, the cucumber is still confused about the torque and precession of the gyroscope.
  • #1
cucumber
20
0
hi. not sure if this belongs in here, so sorry in advance for any trouble caused.
i am in a bit of a predicament with a physics assessment of mine; i need to know the mathematical relationships between the precessional frequency, the couple (or torque, as i have read it called) and the angular momentum of a gyroscope, and (here comes the tricky bit) i would like to understand it...
i just need someone to point me in the right direction, i mean i hardly know which questions to ask or where to start looking (sob sob).
i am quasi-familiar with the concept of moment of inertia being the equivalent of mass in linear motion and angular velocity that of velocity (duh), but i have not found a set of formulae that would allow me to make a connection between the aforementioned...er... things...

i come with the rather unsound basis of a-level physics, which is why it will be an especially challenging task for you get me to understand it. good luck (and thanks).

cucumber.
 
Physics news on Phys.org
  • #2
[tex]\theta r = s[/tex]
[tex]\omega r = v[/tex]
[tex]\alpha r = a[/tex]
[tex]\vec{L} = \vec{r} \times \vec{p}[/tex]
[tex]\vec{\tau} = \vec{r} \times \vec{F}[/tex]

cookiemonster
 
  • #3
thanks cookiemonster.
i'm unsure about a couple of things, though...

what are the "s" and the theta in [theta]*r = s

what are the alpha and the "a" in [alpha]*r = a

what are the "r"'s in both the above equations (just to be sure...)

and finally, what are those two other equations all about?
i suppose that funny looking thing (like half a pi) is torque, but the rest i have absolutely no idea... sorry.
i'd be very grateful if you could clarify them a bit.

thanks again.
cucumber.
 
  • #4
In a circle of radius r the length of any arc is given by the angle it creates with the center of the circle times the radius: [tex]s = \theta r[/tex]

Angular acceleration:
[tex]\alpha = \frac{a_t}{r}[/tex]
http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html#rq

Angular momentum:
[tex]\vec{L} = \vec{r} \times \vec{p}[/tex]
http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

Torque ('tau'):
[tex]\vec{\tau} = \vec{r} \times \vec{F}[/tex]
http://hyperphysics.phy-astr.gsu.edu/hbase/torq2.html#tc

Precession of Gyroscope:
http://hyperphysics.phy-astr.gsu.edu/hbase/gyr.html#gyr
 

1. What is gyroscopic precession?

Gyroscopic precession is the phenomenon where a spinning object, such as a gyroscope, experiences a change in orientation when a force is applied to it. Instead of moving in the direction of the applied force, the gyroscope will rotate perpendicular to the direction of the force.

2. How does gyroscopic precession work?

Gyroscopic precession is based on the principle of angular momentum. When a force is applied to a spinning object, the direction of the force and the direction of the rotation are not parallel. This creates a torque, or rotational force, which causes the object to rotate perpendicular to both the applied force and the original direction of rotation.

3. What is the importance of gyroscopic precession?

Gyroscopic precession is important in many applications, such as navigation systems, gyroscopes used in airplanes and spacecraft, and even in everyday objects like bicycles and toys. It allows for stable and controlled movement, as well as the ability to resist changes in direction.

4. Can gyroscopic precession be explained by Newton's laws of motion?

Yes, gyroscopic precession can be explained by Newton's laws of motion. The first law states that an object will remain at rest or in motion with constant velocity unless acted upon by an external force. The second law states that the force applied to an object is equal to its mass multiplied by its acceleration. The third law states that for every action, there is an equal and opposite reaction. These laws can be applied to explain the torque and resulting rotation in gyroscopic precession.

5. Are there any real-life examples of gyroscopic precession?

Yes, there are many real-life examples of gyroscopic precession. Some common examples include the stability of a spinning top, the controlled movement of a bicycle, and the stability of an airplane in flight. Gyroscopes are also used in navigation systems, satellites, and even in smartphones to detect movement and orientation.

Similar threads

  • Introductory Physics Homework Help
Replies
33
Views
815
  • Introductory Physics Homework Help
Replies
7
Views
745
Replies
7
Views
995
  • Classical Physics
Replies
10
Views
1K
  • Mechanics
Replies
10
Views
1K
Replies
0
Views
474
  • Introductory Physics Homework Help
Replies
1
Views
1K
Replies
23
Views
811
  • Classical Physics
2
Replies
35
Views
3K
Replies
4
Views
1K
Back
Top