Angular momentum about an Axis and a Point

In summary, the conversation discusses the relationship between angular momentum and the parallel axis theorem. It is noted that the direction of angular momentum is dependent on the point of reference, with the vertical component remaining constant. It is also mentioned that the equation for angular momentum is \mathcal{L}= r \times m\mathcal{v} , where the \times represents a cross product.
  • #1
the-ever-kid
53
0
I was wondering if the angular momentum of anybody with constant [itex]\omega[/itex] (angular velocity) about a point on the centre of the circular path and about any point on the axis of rotation is the same...
 
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  • #2
hi the-ever-kid! :smile:

remember the parallel axis theorem

moment of inertia about any axis = moment of inertia about a parallel axis through the centre of mass + md2

where d is the distance between the two parallel axes …

so how does that apply to the angular momentum in the x y and z directions through your two points? :wink:
 
  • #3
i realize what what you just said but what i really wanted to know is like if the direction of the angular momentum is dependent on the point of reference

like suppose an object is rotating in a circle then i know that the angular momentum is [itex]I\omega = L[/itex] and if that point was in the plane itself but still parallel to the axis of rotation then we apply the parallel axis theorem and add the extra md2
term

yes?

but what if that point was on the axis but not in th plane of rotation but either above or below it ...the will the angular momentum be in the same direction?
 
  • #4
d will be different for different directions (through the same point)

(and I'm not sure whether you're envisaging a general case, or eg a rotationally symmetric body rotating about it axis of symmetry)
 
  • #5
http://puu.sh/oyqf [Broken] see O and P
 
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  • #6
If it is a point particle moving in a circle at constant speed (which is what the picture looks like), then there is a simple answer to your question. Use the equation for angular momentum, calculate it around either point and see if there is a difference.

EDIT: which equations do you know for the angular momentum?
 
  • #7
thank you every one got my answer ... i just remembered that [tex]\mathcal{L}= r \times~m\mathcal{v} [/tex] the [itex]\times[/itex] means cross product
[itex]\therefore[/itex] , it will be [itex]\bot[/itex] to the direction of the distance from reference thus as its direction changes it will not be the same as the O

LIKE THIS: http://puu.sh/oyDM [Broken]
 
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  • #8
very good. This result surprised me at first, but it is right. Note that the vertical component of angular momentum stays constant, since the magnitudes of horizontal position and momentum are constant and are always perpendicular to each other. Or speaking more generally, the direction of the shift of the origin is vertical, so the vertical component of angular momentum is unchanged.
 

1. What is angular momentum about an axis?

Angular momentum about an axis is a measure of the rotational motion of a body or system of bodies around a fixed axis. It is a vector quantity that takes into account the mass, velocity, and distance from the axis of rotation.

2. How is angular momentum about an axis calculated?

The formula for calculating angular momentum about an axis is L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. Moment of inertia is a measure of an object's resistance to rotational motion and is dependent on the mass and distribution of mass around the axis of rotation.

3. What is angular momentum about a point?

Angular momentum about a point is a measure of the rotational motion of a body or system of bodies around a fixed point. It is also a vector quantity that takes into account the mass, velocity, and distance from the point of rotation.

4. How is angular momentum about a point different from angular momentum about an axis?

The main difference between angular momentum about a point and about an axis is the reference point. Angular momentum about an axis is calculated with respect to a fixed axis of rotation, while angular momentum about a point is calculated with respect to a fixed point of rotation. Additionally, the moment of inertia used in the calculation may be different for these two types of angular momentum.

5. What are some real-world applications of angular momentum about an axis and a point?

Angular momentum is a fundamental concept in physics and has many practical applications. Some examples include the motion of planets and satellites in space, the spinning of tops and gyroscopes, and the rotation of wheels and gears in machinery. It also plays a crucial role in understanding the stability and control of objects in flight, such as airplanes and rockets.

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