Calculating Angular Momentum and Precession of a Toy Gyroscope

  • Thread starter cuz937100
  • Start date
  • Tags
    Gyroscope
In summary, a toy gyroscope consists of a 2.5 kg disk with a radius of 2 cm mounted on a 7 cm axle and spinning at 47 rev/s. The angular momentum of the disk about its axle is 0.148 and the torque about the point of support due to the weight of the gyro is 1.72. It takes the gyroscope 2π/ω seconds to precess once around. If the radius and length were doubled, it would take 2π/(2ω) seconds for the disk to precess once.
  • #1
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...
 

Attachments

  • gyro.gif
    gyro.gif
    1.8 KB · Views: 672
Last edited by a moderator:
Physics news on Phys.org
  • #2
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.
 
  • #3
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.
 
  • #4
Anymore suggestions? I really need help with this one, I have an exam over this section this week...
 
  • #5
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
 
  • #6
lol, thanks a lot masamune, i already got it though...And I got it before you did ANDREW...
 

Related to Calculating Angular Momentum and Precession of a Toy Gyroscope

What is angular momentum?

Angular momentum is a measure of the rotational motion of an object. It is calculated by multiplying the moment of inertia (a measure of how mass is distributed around an axis of rotation) by the angular velocity (the speed at which the object is rotating).

What is a toy gyroscope?

A toy gyroscope is a spinning object that demonstrates the principles of angular momentum and precession. It typically consists of a spinning disk or wheel mounted on a gimbal, allowing it to rotate freely in any direction.

How do you calculate the angular momentum of a toy gyroscope?

The angular momentum of a toy gyroscope can be calculated by multiplying the moment of inertia of the spinning disk by its angular velocity. The moment of inertia can be calculated using the formula I = mr², where m is the mass of the disk and r is the radius of rotation.

What is precession?

Precession is the phenomenon in which the axis of rotation of a spinning object changes direction. This is caused by an external torque acting on the object, such as gravity or friction.

How does precession affect a toy gyroscope?

Precession causes the axis of rotation of a toy gyroscope to change direction, resulting in a wobbling motion. This is because an external torque, such as friction with the ground, is acting on the spinning disk, causing its axis of rotation to shift. This can be observed in a toy gyroscope as it spins on a flat surface, appearing to "wobble" as it rotates.

Similar threads

Minimal rotational kinetic energy for a gyroscope to precess
    • Introductory Physics Homework Help
Replies
33
Views
1K
Speed of cylinder rolling along a horizontal surface gathering snow (Solved)
    • Introductory Physics Homework Help
Replies
13
Views
943
I Precession of a gyroscope in freefall
    • Mechanics
Replies
10
Views
1K
Why did I get this angular momentum problem wrong?
    • Introductory Physics Homework Help
Replies
25
Views
9K
I Gyroscopic precession of a spin-stabilized bullet
    • Classical Physics
Replies
10
Views
1K
I What does weight actually do in gyroscopic precession?
    • Classical Physics
Replies
7
Views
1K
Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
    • Introductory Physics Homework Help
Replies
30
Views
2K
I Order of rotations: precession, nutation, spin
    • Classical Physics
Replies
3
Views
1K
How Does Angular Momentum Conservation Affect Asteroid Collision Dynamics?
    • Introductory Physics Homework Help
10
Replies
335
Views
8K
Dynamic reaction versus Coriolis acceleration of the disk
    • Introductory Physics Homework Help
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top