Help with angular momentum question

In summary: Therefore, it is important to find the moment of inertia of the rod, which can be calculated using the formula (ML^2)/12, where M is the mass of the rod and L is the length. The length can be found by calculating the distance between the two particles, which is given in the problem as 12m. In summary, to find the angular momentum of the system, we need to calculate the moment of inertia of the rod by using the formula (ML^2)/12, where L is the distance between the two particles, and then use the formula Total angular momentum = (Moment of inertia of rod + moment of inertia of particles) *angular velocity.
  • #1
pakmingki2
35
0
A. At a particular instant, a particle of mass M = 3 kg is at the position (x,y,z) = (4,4,6) m and has velocity (2,1,-2) m/s.

B. An identical particle is placed at (x,y,z) = (-4,-4,-6) m, with velocity (-2,-1,2) m/s.
Find the angular momentum of the pair of particles about the origin.


C. A thin rod of mass 9 kg is added between the two particles (Irod = M L^2/12). Since the particles are moving perpendicular to the line separating them and in opposite directions (you should convince yourself that this is true), then the particles + rod system rotates about its center of mass. Compute the angular frequency of rotation of the rod + particles system.

D. Compute the magnitude of the total angular momentum of the system (particles plus rod).

ok, so i got parts a,b,c pretty easily.

A. <-42, 60, -12>
B. <-84, 120, -24>
C. .363

Ok, so for part D, the main approach i used was total angular momentum = sum of all individual components in the system.

So, i can easily find the angular momentum of the two particles, but the problem is finding the moment of inertia of the thin rod. The formula for inertia is (ML^2)/12, but i can't seem to get the length L from anywhere in the problem.

Any help is appreciated.
thanks alot!
 
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  • #2
Distance between the two particles is the length of the rod.
 
  • #3
how do you find the angular momentum of the particles?
 
  • #4
The angular momentum of the particles = Total moment of inertia*angular velocity=(Moment of inertia of rod + moment of inertia of particles) *angular velocity.
 

1. What is angular momentum?

Angular momentum is a measure of an object's rotational motion. It is a vector quantity that takes into account both the object's mass and its rotational velocity.

2. How is angular momentum calculated?

Angular momentum is calculated by multiplying the object's moment of inertia (a measure of its resistance to rotational motion) by its angular velocity (the rate at which it rotates).

3. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system remains constant unless acted upon by an external torque. This means that if no external forces are acting on a system, its angular momentum will remain the same.

4. How does angular momentum relate to circular motion?

Angular momentum is directly related to circular motion, as objects moving in a circular path have both linear and angular momentum. The direction of an object's angular momentum is perpendicular to its linear momentum and follows the right-hand rule.

5. How can angular momentum be changed?

Angular momentum can be changed by applying an external torque to a system. This can be done by changing the object's moment of inertia, its angular velocity, or both. For example, a spinning figure skater can change their angular momentum by pulling their arms in, decreasing their moment of inertia and increasing their angular velocity.

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