Galileo’s principle and motion in a gravitational field

A reference frame is the body, coordinate system and clock with respect to which motion is described. Frames at rest, or moving with constant velocity in a straight line relative to the Earth, are inertial reference frames. Galileo’s principle of relativity: mechanical processes go the same way in all inertial frames; a mechanical experiment in a closed room cannot show whether the room is at rest or moving uniformly. The rule for adding velocities: the velocity of a body relative to the “rest” frame is υ = u + υ′ (as vectors), where u is the velocity of the moving frame and υ′ is the body’s velocity relative to it. In inertial frames time, mass, acceleration and force are the same (invariant), so Newton’s laws look the same in all of them. A frame that accelerates (or rotates) is non-inertial: to use Newton’s laws there, an inertial force Fᵢ = –m·a (a is the acceleration of the frame) is added to the forces of other bodies. Because of the Earth’s rotation the acceleration at the equator is ≈ 0.034 m/s², much smaller than g, so we take the Earth as approximately inertial.