- #1
welssen
- 6
- 0
Hi there,
I've been trying to solve the following problem, which I found looks pretty basic, but actually got me really confused about the definition of angular momentum.
Problem
The trajectory of a point mass m is described by the following equations, in spherical coordinates:
[itex] r(t) = r_0 + v_0t [/itex]
[itex]\phi(t) = \omega_0t [/itex].
Determine the angular momentum of m (in spherical coordinates).
The attempt at a solution
Angular momentum is defined as [itex] \vec{l} = m\cdot\vec{x(t)}\times\vec{v(t)} [/itex].
Here, I would say, [itex] \vec{x(t)} = r(t)\hat{r} + \phi(t)\hat{\phi} [/itex].
I would take the cross product of this vector with its derivative (the speed) multiplied by mass to get the angular momentum.
But apparently this is wrong. In the given solutions, [itex] \vec{x(t)} = r(t)\hat{r} [/itex]. The angular term is absent.
Could someone explain why the angular term is set to 0 in the cross product of angular momentum?
Thank you.
I've been trying to solve the following problem, which I found looks pretty basic, but actually got me really confused about the definition of angular momentum.
Problem
The trajectory of a point mass m is described by the following equations, in spherical coordinates:
[itex] r(t) = r_0 + v_0t [/itex]
[itex]\phi(t) = \omega_0t [/itex].
Determine the angular momentum of m (in spherical coordinates).
The attempt at a solution
Angular momentum is defined as [itex] \vec{l} = m\cdot\vec{x(t)}\times\vec{v(t)} [/itex].
Here, I would say, [itex] \vec{x(t)} = r(t)\hat{r} + \phi(t)\hat{\phi} [/itex].
I would take the cross product of this vector with its derivative (the speed) multiplied by mass to get the angular momentum.
But apparently this is wrong. In the given solutions, [itex] \vec{x(t)} = r(t)\hat{r} [/itex]. The angular term is absent.
Could someone explain why the angular term is set to 0 in the cross product of angular momentum?
Thank you.