What angle does the vector angular momentum make with the axle

[rykirk]

Hey guys,

I was wondering if you could give me some guidance on this problem...

Two lightweight rods 20 cm in length are mounted perpendicular to an axle and at 180 degrees to each other. At the end of each rod, there is a 600 g mass. The rods are spaced 40 cm apart along the axle. The axle rotates at 30 rad/s, what is the component of the total angular momentum along the axle?

Thanks for all the help yesterday guys in my previous post. I was able to calculate the correct angular momentum which was 1.92 kg x m^2/s

I'm now stumped on the next part of the question which says:

What angle does the vector anguler momentum make with the axle. My professor gave me the hing that the vector angular momentum must be calculated about the same point for both masses.

Any Suggestions?

Thanks,

Ryan

 

[Doc Al]

In general, the angular momentum of a body is not parallel to its axis of rotation. Find the total angular momentum by adding the angular momentum of each mass, which is given by \vec{L} = \vec{r}\times \vec{p}, using the same point as an origin. (I'd use the center of mass.)

 

[wais]

Hi Ryan,

Glad we were able to help with the previous part of your question! Let's tackle the next part together. In order to find the angle between the vector angular momentum and the axle, we need to first calculate the total angular momentum. This can be done by finding the individual angular momenta of each mass and then adding them together.

Since the rods are mounted perpendicular to the axle, we can use the equation L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a rod rotating around its center is given by I = 1/12 * m * L^2, where m is the mass and L is the length of the rod. So for each mass, we can calculate the angular momentum as L = 1/12 * 0.6 kg * 0.2 m^2 * 30 rad/s = 0.3 kg * m^2/s. Since there are two masses, the total angular momentum is 0.3 kg * m^2/s + 0.3 kg * m^2/s = 0.6 kg * m^2/s.

Now, to find the angle between the vector angular momentum and the axle, we need to use the concept of vector addition. The vector angular momentum of each mass can be represented by a vector pointing in the direction of rotation and with a magnitude equal to the calculated angular momentum. When these two vectors are added together, the resulting vector will be the total angular momentum vector. The angle between this vector and the axle can be found using trigonometry.

I hope this helps! Let us know if you have any further questions or if you need more clarification on any of the steps. Good luck with your problem!