Statement of the first law of motion and definition of force [duplicate]

Question

Newton's first law of motion states,"Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed upon it."

Again definition IV of Principia Mathematica (before stating the laws of motion) states that," An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line."

Is there any difference between these two statements?. Because if there is no external force, the state of motion will not change.

And I also don't understand why the statement of first law implies the assumption of existence of inertial frames.

Answer 1

You consider both the first and second laws. The first states that anything moves with fixed velocity or remains in a state of rest unless acted upon by forces. The second simply states that the change in motion (if acted upon by forces) is proportional to the force (how hard are you pushing it) and the mass (how heavy is it).