Deriving relation between angular momentum reduction by torque

In summary, friction can cause a torque that opposes angular momentum, leading to a decrease in angular velocity and momentum. This can be seen in the case of a spinning disk with a changing radial vector and center of mass, resulting in a tippy top-like behavior. Calculating the duration of the disc's stable position and the time it takes to flip the hole position can be done by modifying the moment of inertia in 3 axes and using the theory of the tippy top.
  • #1
caspernorth
28
0
Friction causes a torque that opposes angular momentum. It gets reduced. how can we derive a relation connecting these. friction starts with maximum and becomes zero. angular velocity and its corresponding momentum decreases maximum in the beginning and increases towards the end. the radial vector of friction and center of mass of disk changes from r1 to r2.
 
Physics news on Phys.org
  • #2
It's a bit hard to understand what you're looking for. Say you have a wheel spinning (I) and the only force acting on it is friction acting to slow it down. The angular acceleration due to the frictional torque is given by Torque = I*alpha.
 
  • #3
I knew it would be hard, sorry. Let me phrase it in a simple way.
There is a disc with a hole (I recently posted here asking for its moment of inertia). It is spinning about an axis passing through its own diameter. Due to the shift in point of contact and center of mass the disc scratches the ground and this friction creates a torque opposing the angular frequency. (angular momentum in the direction). this opposing is happening when the center of mass is on the bottom. This friction will also bring the center of mass upwards (like a tippie top) till the line of center of mass co-incides with the sliding point.
()
Now friction decreases, angular frequency goes back to normal and meanwhile a change in radial vector also occured. (from center of mass to diameter minus center of mass).

how can all these changes expressed in an equation.
 
Last edited by a moderator:
  • #4
W = integral of (torque x dθ) = Iω^2 / 2
Considering change in torque is difficult i guess. since Radial vector changes and the dθ is infact a tilt to backwards... so I guess we need a much complicated differential equation, isn't that so?
Change in torque is rather uncommon in such cases right? is this a case of change in acceleration-jerking. I've never seen an equation including jerking.
 
  • #5
This reminds me of (and I suspect that it's equivalent to) the infamous "tippy top" toy. The analysis is non-trivial.

https://www.youtube.com/watch?v=AyAgeUneFds
 
  • #6
Doc Al said:
This reminds me of (and I suspect that it's equivalent to) the infamous "tippy top" toy. The analysis is non-trivial.

https://www.youtube.com/watch?v=AyAgeUneFds

But, after going through the tippie top's theory
:http://ckw.phys.ncku.edu.tw/public/...ons/Tippy Top/Gray-Nickel_AJP68-821(2000).pdf

I think a similar case can be applied here, except that the moment of inertia in 3 axes would have to be modified to suit the disk. what do you think?
 
  • #7
By the way, I need a help in doing a project based on this(the disc's strange behaviour and similar objects like tippy-top). How can i include a sample calculation that shows how long the disc will stay in its stable position, how much time will it take to flip the hole position. How can i make the topic presentable.
any ideas on this, please help.
 

1. What is angular momentum reduction by torque?

Angular momentum reduction by torque is the decrease in the angular momentum of an object due to the application of a torque, or twisting force. It is a measure of the rotational motion of an object and is calculated by multiplying the moment of inertia by the angular velocity.

2. How is the relation between angular momentum and torque derived?

The relation between angular momentum and torque is derived using the basic principles of rotational dynamics. It is derived from the definition of torque as the cross product of force and distance, and the definition of angular momentum as the product of moment of inertia and angular velocity.

3. What is the equation for the relation between angular momentum reduction and torque?

The equation for the relation between angular momentum reduction and torque is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

4. How does torque affect the angular momentum of an object?

Torque affects the angular momentum of an object by changing its rotational motion. When a torque is applied to an object, it causes a change in its angular velocity, which in turn affects the object's angular momentum.

5. What are some real-world applications of the relation between angular momentum reduction and torque?

The relation between angular momentum reduction and torque is important in many real-world applications, such as in the design of vehicles and machinery that rotate, like cars, airplanes, and turbines. It is also essential in understanding the behavior of spinning objects in space, such as satellites and planets.

Similar threads

Conceptual questions about Angular Momentum Conservation and torque
    • Mechanics
Replies
2
Views
1K
I Conservation of angular momentum during collisions
    • Mechanics
Replies
3
Views
1K
2-body problem - conservation of angular momentum
    • Mechanics
2
Replies
40
Views
2K
I Transmission of torque using friction
    • Mechanics
Replies
32
Views
769
Conservation of Angular Momentum is Dumbfounding
    • Mechanics
2
Replies
36
Views
14K
Conservation of Angular Momentum on a rotating disc
    • Mechanics
Replies
22
Views
3K
Conservation of angular momentum and its counterpart for linear momentum
    • Mechanics
Replies
13
Views
2K
I How to transfer angular momentum between two flywheels?
    • Mechanics
Replies
8
Views
2K
Conservation of Angular Momentum
    • Mechanics
Replies
9
Views
1K
Torque and Angular Momentum Vector Question.
    • Mechanics
Replies
1
Views
902

Hot Threads

Recent Insights

Back
Top