# Angular momentum relative to the origin

• JessicaHelena
In summary, the angular momentum of a 2.4 kg particle-like object with velocity components of vx = 25 m/s and vy = 80 m/s at the point with coordinates (3.0, -4.0) m can be found by taking the cross product of the position vector and momentum vector. The resulting value is -816k.

## Homework Statement

A 2.4 kg particle-like object moves in a plane with velocity components vx = 25 m/s and vy = 80 m/s as it passes through the point with (x, y)coordinates of (3.0, −4.0) m. (Express your answers in vector form.)
(a) What is its angular momentum relative to the origin at this moment?

L=pxr

## The Attempt at a Solution

I did 2.4*the 3x3 matrix
i j k
25 80 0
3 -4 0
and this gave me 2.4*(-100-240)k = -816k.

[FONT=verdana, geneva, sans-serif]When I entered this in, I got this wrong, but without the minus sign (so 816k), the webassign accepted this as correct. However, this bothers me because isn't the correct sign supposed to be negative? [/FONT]

JessicaHelena said:

## Homework Equations

L=pxr

##\vec{L} = \vec{r} \times \vec{p}##

Surely?

Ah, right... r x p doesn't equal p x r and I memorised the formula the wrong way. Thank you.

JessicaHelena said:
Ah, right... r x p doesn't equal p x r and I memorised the formula the wrong way. Thank you.

If you start from a point, the ##\vec{r}## displacement comes first. If you follow this you reach the particle, where you find the momentum ##\vec{p}##.

That's how I remember it.

## 1. What is angular momentum relative to the origin?

Angular momentum relative to the origin is a measure of the rotational motion of an object around a fixed point, or origin. It takes into account the object's mass, velocity, and distance from the origin.

## 2. How is angular momentum relative to the origin calculated?

The formula for calculating angular momentum relative to the origin is L = mvr, where L is the angular momentum, m is the mass of the object, v is the velocity, and r is the distance from the origin.

## 3. Why is angular momentum relative to the origin important in physics?

Angular momentum relative to the origin is important because it is a conserved quantity in a closed system, meaning it remains constant unless acted upon by an external force. This makes it a useful tool in understanding and predicting the behavior of rotating objects.

## 4. How does angular momentum relative to the origin differ from linear momentum?

Angular momentum relative to the origin is a vector quantity that takes into account both the direction and magnitude of rotational motion, while linear momentum only considers an object's linear motion. Additionally, angular momentum is calculated relative to a fixed point, while linear momentum is calculated relative to an object's center of mass.

## 5. How is the conservation of angular momentum related to the conservation of energy?

The conservation of angular momentum is closely related to the conservation of energy. In a closed system, angular momentum and energy are both conserved, meaning they cannot be created or destroyed, only transferred between different forms. This relationship can be seen in many physical phenomena, such as the spin of a spinning top or the rotation of planets around the sun.