Final answer:
The angular momentum of a particle is the cross product of its position vector and linear momentum vector. To find it, calculate the particle's linear momentum by multiplying its mass (in kg) by its velocity vector, then use the cross product to find the angular momentum about the origin.
Step-by-step explanation:
The angular momentum of a particle about a point is given by the cross product of the position vector ℝ (ℝ = 4ᵢ + 3ᵣ - 2ᵤ in this case) and the linear momentum vector ℒ of the particle, where ℒ is the product of the mass m and the velocity vector ᵔ (ᵔ = 5ᵢ - 2ᵣ + 4ᵤ in this case). First, we calculate the linear momentum by multiplying the mass (converted to kg) by the velocity vector. Then, we find the cross product of the position vector and the linear momentum vector. The formulas are as follows:
For our example, the mass m = 500 g = 0.5 kg. So the linear momentum ℒ equals (0.5 kg × ᵔ). The cross product is calculated using the determinant of the matrix composed of the unit vectors ᵢ, ᵣ, ᵤ and the components of the vectors ℝ and ℒ. With the given vectors, the calculation of angular momentum will produce a vector representing the angular momentum about the origin for the given particle.