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I got a problem which asks if the speed of a car in Oslo is 50km/hr what will be its speed when viewed from space.

I have the relation between the velocities as observed from inertial and non-inertial frames of references as follows $$ \vec{v} I=\vec{v} R+\vec{\omega}\times\vec{r} , $$ where $I$ and $R$ stand for inertial and rotating frames, $\vec{r}$ is the position vector and $\vec{\omega}$ is the angular velocity. Am I short with information to solve it since I need to know the angle between the vectors?

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    $\begingroup$ Try to fix the math formatting using MathJax. Look at the help under physics.stackexchange.com/help/notation $\endgroup$
    – John Alexiou
    Commented Nov 4, 2016 at 5:00
  • $\begingroup$ Oslo is a place in space. So, the speed of the car when viewed from Oslo is a perfectly good answer. That's 50 km/hr. This is what's called "ground speed", relative to nearby dirt... $\endgroup$
    – Whit3rd
    Commented Nov 4, 2016 at 5:53
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    $\begingroup$ Is the viewer in geosynchronous orbit, inside the ISS or just passing through at 0.1c on her way to Alpha Centauri? $\endgroup$
    – RedGrittyBrick
    Commented Nov 4, 2016 at 17:14
  • $\begingroup$ You are missing some vital information :What direction is the car travelling? Where is the observer and how is he/she moving? "Space" is not a frame of reference. $\endgroup$
    – sammy gerbil
    Commented Nov 4, 2016 at 21:15

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Yes you need the angle of the car direction relative to the East West direction. If the car moves eastward then the speed is added. But if the car is moving northwards then you need to add the tangential speed of the earth vectorially to the velocity of the car.

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You do need to know the direction in which the car is travelling, the period of the Earth's rotation, the radius of the Earth and the latitude of Oslo ($\approx 60^\circ $ N).

You need to know the latitude so that you can find the radius of the path of the car in Oslo about the Earth's axis of rotation.
The radius would be the Earth's radius if the car had been on the Equator and zero if the car had been at a geographic pole.

The velocity of the car relative to you is equal to the velocity of the car relative to the Earth $+$ velocity of the Earth relative to you.
That has be a vector addition.

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