torque maths

This example in the textbook derives the rate of change of area using angular momentum but there is some maths that doesn't make sense and it is really bugging me. Maybe someone can explain and relieve me of frustration.

L=(rXmv)=rrhatXm(rdotrhat+rphoetadotphoetahat) = mr^2 phoetadotkhat

sorry about notation, dont know how to use latex.

Anyway the first term in the bracket cancels because it is the cross product and the angle is 0, but for the second term, dont you need to take the magnitude of rrhat and mrphoetadotphoetahat and multiply that by sin90=1, or use determinants? and if you use determinants, how? coz it is in polar co-ordinates and i dont know how to do it.

Reply 1

Morbo

17

PHKnows

This example in the textbook derives the rate of change of area using angular momentum but there is some maths that doesn't make sense and it is really bugging me. Maybe someone can explain and relieve me of frustration.

\\\vec{L} = \vec{r} \times m\vec{v}

The velocity can be split into the radial and angular components, which are perpendicular. Radial velocity is simply the rate of change of radius in the radial direction. Angular velocity we can get from: