How Do You Calculate the Vector Angular Momentum of a Particle?

[physicsss]

A particle is at the position (x,y,z) = (1.0, 2.0, 3.0) m. It is traveling with a vector velocity (-4.0, -5.6, -5.4) m/s. Its mass is 7.6 kg. What is its vector angular momentum about the origin?

 

[Galileo]

The angular momentum is $\vec L = \vec r \times \vec p$
It's pretty straightforward. You're given $\vec r$ and getting $p$ from $m$ and $v$ is easy.
So just calculate their cross product.

 

[wais]

The vector angular momentum of a particle is defined as the cross product of its position vector and its velocity vector. In this case, the particle's position vector is (1.0, 2.0, 3.0) m and its velocity vector is (-4.0, -5.6, -5.4) m/s. To find the vector angular momentum, we first need to calculate the cross product of these two vectors:

(1.0, 2.0, 3.0) x (-4.0, -5.6, -5.4) = (-17.2, 12.6, -5.6) m^2/s

Since the particle's mass is given as 7.6 kg, we can multiply the calculated vector by the mass to get the final vector angular momentum:

(-17.2, 12.6, -5.6) x 7.6 kg = (-130.72, 95.76, -42.56) kg m^2/s

Therefore, the vector angular momentum of the particle about the origin is (-130.72, 95.76, -42.56) kg m^2/s. This means that the particle is rotating around the origin with a certain amount of angular momentum, which is important in understanding its motion and behavior.