What Angle Does the Angular Momentum Vector Make with the Axle?

In summary, for part 2, the component of the total angular momentum along the axle is 2mL^2w. For part 3, in order to find the angle that the vector angular momentum makes with the axle, we need to calculate the total angular momentum about the center of mass by adding the angular momentum of each mass, which is given by \vec{L} = \vec{r}\times \vec{p}. The masses may also rotate counter-clockwise due to their weight, so the angle may not be 0.
  • #1
pixelized
7
0
I solved for 2 correctly but I can't figure out what to do for #3 Any help would be much appreciated. I think it might involve L = r x p , but I'm not entirely sure.

2. [1pt]
Two lightweight rods L = 20.5 cm in length are mounted perpendicular to a vertical axle and at 180° to each other (see figure below).

At the end of each rod is a m = 602 g mass. The rods are spaced h = 35.7 cm apart along the axle. The axle rotates at 28.7 rad/s such that the angular velocity vector points upward (+). What is the component of the total angular momentum along the axle?

3. What angle does the vector angular momentum make with the axle?
 

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  • #2
Did you get [tex]2mL^2w[/tex] for part 2?

If it's only rotating about the vertical axle... then the answer in part 2 seems to be the only component so it seems to me the angle is 0.

I'm wondering if the masses are also allowed to rotate counter-clockwise (due to their weight).
 
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  • #3
yes that's what I used for part two.

I tried 0 but it was wrong. So maybe they can rotate counter clockwise. How would that work?
 
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  • #4
pixelized said:
I solved for 2 correctly but I can't figure out what to do for #3 Any help would be much appreciated. I think it might involve L = r x p , but I'm not entirely sure.
In general, the angular momentum of a body is not parallel to its axis of rotation. Find the total angular momentum about the center of mass by adding the angular momentum of each mass, which is given by [itex]\vec{L} = \vec{r}\times \vec{p}[/itex].
 

Related to What Angle Does the Angular Momentum Vector Make with the Axle?

1. What is the definition of angle of angular momentum?

The angle of angular momentum is the orientation of the axis around which a body is rotating. It is a measure of how the direction of rotation changes with time.

2. How is the angle of angular momentum related to the conservation of angular momentum?

The angle of angular momentum is directly related to the conservation of angular momentum. This means that the magnitude and direction of the angular momentum of a system will remain constant unless acted upon by an external torque.

3. How is the angle of angular momentum calculated?

The angle of angular momentum is calculated by taking the cross product of the position vector and the momentum vector. It is typically measured in radians or degrees.

4. What is the importance of the angle of angular momentum in rotational motion?

The angle of angular momentum is important in rotational motion because it determines the axis of rotation and the direction of rotation. It is also crucial in understanding the stability and conservation of angular momentum in a system.

5. How does the angle of angular momentum affect the moment of inertia?

The angle of angular momentum is directly related to the moment of inertia, which is a measure of an object's resistance to rotational motion. A larger angle of angular momentum will result in a larger moment of inertia, making it more difficult to change the object's rotational motion.

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