If the earth spins at roughly 1,118.4 mi/h and you are speeding down the highway at 115 mi/h, what does a cop's radar read? Hypothetically, if the earth spins at roughly 1,118.4 mi/h and you are speeding down the highway at 115 mi/h, what does a cop's radar read?
Also, if the earth is spinning at 1,118.4 mi/h and you are speeding down the highway in the opposite direction at 115 mi/h, what does the cop's radar read if they were on the moon?
 A: Note that 1,118.4 miles per hour is the tangential, or linear speed of the earth's surface (at the equator). The earth spins at approximately 360$^\circ$ per 24 hours, or 15$^\circ$ per hour ($\approx 0.004^\circ\ s^{-1}$).
The cop’s radar (assuming the cop is stationary$^1$) will read whatever speed you are moving relative to the earth's surface. That is, 115 miles per hour. The surface of the earth is taken to move at zero mph for observers on the earth's surface. In other words, the earth's surface forms a stationary frame of reference for all observers on the earth's surface.
Now if you’re an observer (the cop) on the moon, the speed the radar would detect will be the tangential speed of the earth's surface, plus the speed of the car (ignoring the orbital motion of the moon).
So for an observer on the moon, if the car is moving at a speed 115 miles per hour opposite to the direction of rotation of the earth (at equator), then its resultant speed will be (1,118.4 - 115)=1,003.4 miles per hour.
If the car was on the moon and the radar was on earth, then the same idea applies. But we now need to add the additional motion of the moon around the earth (taking the earth to be stationary). That is, the resultant speed will be $$v_r=v_t+v_c+v_o$$ where $v_t$ is the tangential speed of the moon's surface, and $v_c$ is the speed of the car relative to the moon’s surface and $v_o$ is the tangential speed of the moon's orbital motion.
$^1$ If the cop car is moving, the officer would be using "moving radar" and the radar gun must also register the speed of the policeman's car to determine the the speed of the other car. A Doppler shift will occur in the frequency that the radar gun receives after it bounces of the moving car. The radar gun device will measure this change in frequency, and is programmed to then calculate the speed of the car.
