# Angular Momentum of a system of particles relative to another point

• DarkerStorm
In summary, two particles with masses of 23 kg and 64 kg are moving in opposite directions along a straight line. The total angular momentum of the system about the z-axis, relative to point B along the y-axis, is -43340 kgm2/s when the distance from point B is 22 meters.
DarkerStorm

## Homework Statement

Two particles move in opposite directions along a straight line. Particle 1 of mass m1 = 23 kg at x1 = 16 m moves with a speed v1 = 34 m/s (to the right), while the particle 2 of mass m2 = 64 kg at x2 = −25 m moves with a speed v2 = −43 m/s (to the left). Given: Counter-clockwise is the positive angular direction.

1)What is the total angular momentum of the system about the z-axis relative to point A along y-axis if d1 = 13 m? Answer in units of kgm2/s.

2) What is the total angular momentum of the system about the z-axis relative to point B along y-axis if d2 = 22 m? Answer in units of kgm2/s.

m1 = 23
Position1 = {16 i, 0 j, 0 k}
v1 = {34 i, 0 j, 0 k}

m2 = 64
Pos2 = {-25 i , 0 j, 0 k}
v2 = {-43 i, 0 j, 0 k}

d1 = {0 i, -13 j, 0 k}
d2 = {0 i, 22 j, 0 k}

## Homework Equations

L = Position $$\times$$ m v

## The Attempt at a Solution

I got number 1 correct, and number 2 should be the same. however just changing d1 to d2 does not give the correct answer.

1)
{16, 0 , 0} + {0, -13, 0} = {16, -13, 0}
{-25 , 0, 0}+ {0, -13, 0} = {-25, -13, 0}

{16, -13, 0} $$\times$$ (23 {34 , 0 , 0 }) +
{-25, -13, 0} $$\times$$ (64 {-43 , 0 , 0 }) = {0, 0, -25610} = 25610 k

2) should be the same but I get {0, 0, 43340} which is incorrect

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Welcome to PF!

Hi DarkerStorm! Welcome to PF!
DarkerStorm said:
1)
{16, 0 , 0} + {0, -13, 0} = {16, -13, 0}
{-25 , 0, 0}+ {0, -13, 0} = {-25, -13, 0}

{16, -13, 0} $$\times$$ (23 {34 , 0 , 0 }) +
{-25, -13, 0} $$\times$$ (64 {-43 , 0 , 0 }) = {0, 0, -25610} = 25610 k

2) should be the same but I get {0, 0, 43340} which is incorrect

Looks ok to me (opposite sign to 1), of course).

(btw, you could have omitted the {16, 0 , 0} and {-25, 0 , 0} )

hmm … you could try 43440, in case someone hit the wrong key.

Thanks the problem was that number 2 have to be negative.

## 1. What is angular momentum of a system of particles relative to another point?

Angular momentum is a measure of the rotational motion of a system of particles around a specific point. It is the product of the mass, velocity, and distance from the point of rotation of each particle in the system.

## 2. How is angular momentum different from linear momentum?

Angular momentum involves the rotational motion of particles, while linear momentum involves their linear motion. Angular momentum also takes into account the distance from the point of rotation, while linear momentum only considers the velocity of the particles.

## 3. What is the equation for calculating angular momentum?

The equation for calculating angular momentum is L = Iω, where L is angular momentum, I is the moment of inertia, and ω is the angular velocity of the system.

## 4. How does the distribution of mass affect the angular momentum of a system?

The distribution of mass within a system can affect its moment of inertia, which in turn affects the angular momentum. A system with more mass farther away from the point of rotation will have a higher moment of inertia and therefore a higher angular momentum.

## 5. Can angular momentum be conserved in a system of particles?

Yes, angular momentum is conserved in a closed system, meaning there are no external torques acting on the system. This is known as the law of conservation of angular momentum.

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