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LECTURE #12 – SUMMARY

Section III.2 Inertial vs. Noninertial Reference Frames 's Laws of do not hold (1) when v ≈ c, i.e., motion near the of light (2) in non-inertial reference frames, i.e., in accelerating frames of reference References frames which move at constant = inertial frames of reference. object of m Let's say that A is an inertial . P       P vP = vP + v A and aP = aP + aA vA B A B B A B A First Case: vB is constant ⇒ then B is also an inertial frame of reference vB    A vP = vP + v A so A and B measure different  B  A B A observerB observer P = P aB aA so A and B measure the same     ∴ P = P = maB maA and FA FB So observers in different inertial reference frames agree on the net on P. P = ⇒ P = Special case: aA 0 then aB 0. Both observers say no acts on P. This means that • velocities can be different in different inertial frames of reference, but • and CANNOT differ in different inertial reference frames ∴ "rest" is relative: can only measure relative velocities of inertial reference frames Case: v A is NOT constant ⇒ then B is a non-inertial reference frame    B vP = vP + v A so A and B still measure different velocities  B  A  B aP = aP + aA so A and B now measure different accelerations B  A B     ∴ P = P + A = + maB maA maB and FB FA Ff Observer B sees a different force applied to P than the force that observer A sees. Observer B is mistaking his/her own acceleration for that of the object. error = F = maA =   f  B  P at rest w.r.t. A aP = aP + aA = 0 + aA B A B  B   = P ∴ = A = − B FB maB FB maB maA Two interpretations: aB 0 (1) a force of unknown origin is accelerating P w.r.t. B A A B (2) observer B is accelerating and object P only APPEARS to be accelerating

Therefore, we conclude that Newton's Laws of motion do not hold in non-inertial frames of reference. Do NOT apply "F = ma" in accelerating frames of reference ! ______PHY 140Y – Foundations of Physics, Fall Term 2001 (K. Strong) Lecture 12