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hi, I'm currently doing a mechanics module at Uni. The thing is, I'm not very sure about rules regarding the vector cross product and dot product.

For example, it says in my notes for angular momentum:

"Introducing polar coordinates

[tex] \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi \mathbf{j}) [/tex]

[tex] \mathbf{\dot{r}} = \dot{r} (cos \Phi \mathbf{i} + sin \Phi \mathbf{j}) + r \dot{\Phi}(-sin \Phi \mathbf{i} + cos \Phi \mathbf{j})[/tex]

The angular momentum about 0 is given by

[tex] \mathbf{h} = m \mathbf{r} \times \mathbf{\dot{r}} = mr^2 \dot{\Phi} \mathbf{k} [/tex]"

How do you get all those sin and cos functions to cancel out?! I mean what's going on here? How did the k suddenly appear?

For example, it says in my notes for angular momentum:

"Introducing polar coordinates

[tex] \mathbf{r} = r(cos \Phi \mathbf{i} + sin \Phi \mathbf{j}) [/tex]

[tex] \mathbf{\dot{r}} = \dot{r} (cos \Phi \mathbf{i} + sin \Phi \mathbf{j}) + r \dot{\Phi}(-sin \Phi \mathbf{i} + cos \Phi \mathbf{j})[/tex]

The angular momentum about 0 is given by

[tex] \mathbf{h} = m \mathbf{r} \times \mathbf{\dot{r}} = mr^2 \dot{\Phi} \mathbf{k} [/tex]"

How do you get all those sin and cos functions to cancel out?! I mean what's going on here? How did the k suddenly appear?

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