Angular Momentum of Two Particle System

In summary, the conversation discusses the concept of angular momentum in a system of two particles connected by a rigid rod and a spinning stick. The attempt at a solution involves finding the angular momentum for each particle separately and then adding them together, but this is incorrect as angular momentum is a vector. The correct approach would involve treating them as vectors and applying Newton's second law, which would reveal that the angular momentum is not conserved due to the three-dimensional nature of the problem.
  • #1
Kites
39
0

Homework Statement



Consider a particle of mass m and a particle of mass 2m. They are connected by a horizontal, massless, rigid rod of length 2a. The rod is fixed to a vertical stick that connects to the rod's midpoint. The stick is spinning with constant angular speed.

Consider a point P, located on the stick a distance d below the rod. Show that angular momentum of the two particle system, when taken about point P, is not conserved.

Homework Equations



L = r X p

theta = 90 degrees

The Attempt at a Solution



So what I've done is find angular momentum for either mass, separately.
Doing the following:

L_1 = R x P
= |r||p| sin(theta)
= (a^2+d^2)^(1/2)* ma(omega)

L_2 = R x P
= |r||p| sin(theta)
= (a^2+d^2)^(1/2)*2ma(omega)

What I want to do... by intuition... is just add these two together. but they're magnitudes not vectors... so i am a bit confused if I can.

If not, what the heck do I do?
 
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  • #2
angular momentum is a vector

Kites said:
L_1 = R x P
= |r||p| sin(theta)
= (a^2+d^2)^(1/2)* ma(omega)

L_2 = R x P
= |r||p| sin(theta)
= (a^2+d^2)^(1/2)*2ma(omega)

What I want to do... by intuition... is just add these two together. but they're magnitudes not vectors... so i am a bit confused if I can.

If not, what the heck do I do?

Hi Kites! :smile:

Angular momentum is a vector (strictly, a pseudovector), not a scalar …

it's the cross-product of two vectors! :smile:

The moment form of good ol' Newton's second law is Net Torque = rate of change of angular momentum … and both sides of the equation are (pseudo-)vectors. :biggrin:

Most exam questions on angular momentum are two-dimensional, so the angular momentums are all perpendicular to the plane of the exam paper, and you can just add them!

But this question is three-dimensional … so you must treat them like the vectors they really are. :smile:

(btw, applying Newton's second law, can you see why it's not conserved? :wink:)
 

1. What is angular momentum of a two particle system?

Angular momentum is a physical quantity that represents the rotational motion of a system. In a two particle system, it is the measure of the total rotational momentum of the two particles around their common center of mass.

2. How is angular momentum calculated in a two particle system?

The angular momentum of a two particle system is calculated by multiplying the relative distance between the two particles by their individual linear momentum and the sine of the angle between them.

3. Is angular momentum conserved in a two particle system?

Yes, according to the law of conservation of angular momentum, the total angular momentum of a two particle system remains constant unless an external torque is applied.

4. What factors affect the angular momentum of a two particle system?

The angular momentum of a two particle system can be affected by the masses, velocities, and relative positions of the two particles. External forces or torques acting on the system can also change its angular momentum.

5. How is angular momentum used in physics and engineering?

Angular momentum is an important concept in many fields of physics and engineering, including rotational motion, orbital mechanics, and fluid dynamics. It is used to describe and predict the behavior of rotating objects and systems, such as planets, satellites, and spinning machinery.

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