GRE Physics Companion: Reference Frames in Newtonian Mechanics

This companion is attached to M00-06 and contains only GRE-oriented strategy and speed practice. The core mechanics concepts, derivations, and ordinary problems belong in M00-06.

1 Fast frame triage

For a short mechanics question, first ask whether the second frame is related to the first by constant translational velocity, translational acceleration, or rotation.

The three most useful formulas are

(1)

(2)

and

(3)

If V is constant, then A = 0 and

(4)

That single observation resolves many timed questions immediately.

2 High-frequency GRE traps

1. Constant relative velocity changes measured velocity but not acceleration.
2. Equal acceleration in two Galilean frames does not imply equal velocity.
3. Displacement of one particle over the same time interval is generally frame dependent.
4. In an accelerating frame, the inertial force is opposite the frame acceleration: −mA.
5. Constant angular speed does not make a rotating frame inertial.

3 Worked GRE example 1: identify the invariant

Two inertial frames move at constant relative velocity. Which quantity for a given particle must have the same value in both frames: position, velocity, momentum, kinetic energy, or acceleration?

Because the transformation velocity is constant,

(5)

The correct choice is acceleration. The other listed quantities generally change under a Galilean transformation.

4 Worked GRE example 2: accelerating-frame sign

A free 2 kg mass is observed from a CAR accelerating east at 3 m∕s². What apparent force is assigned to the mass in the car frame?

For a free particle, a = 0 in an inertial frame. Therefore

(6)

The apparent force is

(7)

Its magnitude is

(8)

directed west.

5 GRE-speed questions

M00-06G-Q01

Frame S′ moves east at 10 m∕s relative to S. A particle moves east at 14 m∕s in S. Its velocity in S′ is

(A) 4 m∕s east (B) 4 m∕s west (C) 10 m∕s east (D) 14 m∕s east (E) 24 m∕s east.

M00-06G-Q02

Two inertial frames are related by a Galilean transformation. Which quantity for a particle is necessarily identical in both?

(A) position (B) velocity (C) acceleration (D) momentum (E) kinetic energy.

M00-06G-Q03

A car accelerates north at 2 m∕s². A free 3 kg object is described in the car frame. The inertial-force term is

(A) 6 N north (B) 6 N south (C) 3 N north (D) 3 N south (E) zero.

M00-06G-Q04

A disk rotates at constant angular speed. A point fixed to the disk is stationary in the disk frame. Which statement is correct?

(A) The disk frame is inertial because the point is stationary.
(B) The disk frame is inertial because angular speed is constant.
(C) The point has zero acceleration in every frame.
(D) The disk frame is non-inertial because a fixed point can have centripetal acceleration in an inertial frame.
(E) Newtonian mechanics cannot describe the disk.

M00-06G-Q05

A passenger walks at 2 m∕s forward inside a train moving at 18 m∕s relative to the ground. The passenger speed relative to the ground is

(A) 2 m∕s (B) 16 m∕s (C) 18 m∕s (D) 20 m∕s (E) 36 m∕s.

6 Answers and brief rationales

1. Q01: A. Use u′ = u − V = 14 − 10 = 4 m∕s east.
2. Q02: C. Constant relative velocity implies a′ = a.
3. Q03: B. F_inertial = −mA, so the direction is south and the magnitude is 6 N.
4. Q04: D. Rotation makes the frame non-inertial even when angular speed is constant.
5. Q05: D. u = V + u′ = 18 + 2 = 20 m∕s.

References