Similarly, is $F=\frac{dp}{dt}$ valid in non-inertial frames? If not, then why? Surely, we can write $P=mv$ and $L=Iω$ in non-inertial frames.
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@KP99 my book says that the torque equation is invalid, but the angular momentum equation is valid. – CallousCalculus Feb 22 '23 at 05:56
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1See https://physics.stackexchange.com/q/186317/ – KP99 Feb 22 '23 at 06:10
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@KP99 I know how to calculate torques in non-inertial frames, I want to know why is it that $τ=dL/dt$ is invalid but $L=Iω$ is valid and whether this applies to translational motion. – CallousCalculus Feb 22 '23 at 06:16
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In body fixed system is the angular momentum $~\dfrac{dL}{dt}=\dfrac{dL}{d\tau }+\omega \times L=\tau ~$ . The components of the torque is given in body system – Eli Feb 22 '23 at 08:23
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See if you start from $\tau=r\times F$, then you see that $F$ can transform non-trivially under change of co-ordinate system, giving rise to certain "fictitious" terms, which is solely due to our choice of reference frame. E.g. Coriolis force – KP99 Feb 22 '23 at 10:56