Is spin angular momentum increasing in a gyroscope?

In summary, the conversation discusses the equation for precession frequency in a textbook and the discrepancy in the derivation of this equation. The speaker also raises a question about the relationship between spin angular momentum and precession frequency, and the response emphasizes the conservation of angular momentum and the possibility of changes in moment of inertia.
  • #1
applestrudle
64
0
In my textbook there is an equation for the precession frequency:

Ω = τ/Iω

The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t = delta t)

If the spin angular momentum is increasing with time wouldn't that means the precession frequency would be decreasing but my textbook says constant velocity

:confused:
 
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  • #2
I'm not sure what you are asking, but angular momentum is conserved, so it can't increase without some external torque. The moment of inertia could change if the gyroscope changes shape, but the angular momentum should stay constant, or be slowly decreasing due to friction.
 

FAQ: Is spin angular momentum increasing in a gyroscope?

What is spin angular momentum?

Spin angular momentum is a property of rotating objects that measures the amount of rotational motion they possess. It is defined as the product of an object's moment of inertia and its angular velocity.

How is spin angular momentum different from orbital angular momentum?

Spin angular momentum refers to the rotation of an object around its own axis, while orbital angular momentum refers to the rotation of an object around another object.

Does spin angular momentum increase in a gyroscope?

Yes, spin angular momentum increases in a gyroscope as it rotates due to conservation of angular momentum. As the gyroscope spins faster, its spin angular momentum also increases.

What is the relationship between spin angular momentum and gyroscopic stability?

Spin angular momentum is directly related to gyroscopic stability. A gyroscope with a higher spin angular momentum will have greater stability and will be able to resist external forces more effectively.

Can spin angular momentum be controlled in a gyroscope?

Yes, spin angular momentum in a gyroscope can be controlled by adjusting the rotation speed or direction of the gyroscope. This can be achieved through external forces, such as torque, or by manipulating the internal components of the gyroscope.

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