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1.4 Reference Frames and Relative Motion

Syllabus
2024
Topic
1.4
Level
—

Learning objectives

1.4B—Describe the motion of objects as measured by observers in different inertial reference framesDescribe the motion of objects as measured by observers in different inertial reference frames.• Measurements from a given reference frame may be converted to measurements from another reference frame.• The observed velocity of an object results from the combination of the object’s velocity and the velocity of the observer’s reference frame.- i. Combining the motion of an object and the motion of an observer in a given reference frame involves the addition or subtraction of vectors.- ii. The acceleration of any object is the same as measured from all inertial reference frames.1.4A—Describe the reference frame of a given observerDescribe the reference frame of a given observer.• The choice of reference frame will determine the direction and magnitude of quantities measured by an observer in that reference frame. TOPIC 1.4 Reference Frames and Relative Motion

Relative velocity subtracts the observer’s motion

Name the frame

For one-dimensional motion, an observer measures the object’s velocity relative to the observer’s own frame. Choose a positive direction and keep every velocity signed.

Subtract the observer velocity

vobject/observer=vobject/ground−vobserver/groundv_{\text{object/observer}}=v_{\text{object/ground}}-v_{\text{observer/ground}}

Hypothetical example: east is positive. A passenger walks east at +2 m s−1+2\,\mathrm{m\,s^{-1}} relative to a train moving east at +10 m s−1+10\,\mathrm{m\,s^{-1}} relative to the ground. The passenger’s ground velocity is +12 m s−1+12\,\mathrm{m\,s^{-1}}; equivalently, a ground observer moving at 0 measures 12 m/s east, while a train observer measures 12−10=+2 m s−112-10=+2\,\mathrm{m\,s^{-1}}.

What changes—and what does not

Velocity can differ between inertial frames, but acceleration is the same in all inertial frames. AP Physics 1 restricts relative-velocity vector addition or subtraction to one dimension and assumes the stated frame is inertial unless told otherwise.

A reference frame fixes who measures motion—and how

Define the observer’s coordinates

A reference frame is the coordinate system and clock attached to an observer. Identify the observer, origin, positive axis and time reference before describing position or velocity.

Compare the same event

Same event Ground frame Train frame
Train moving east at 10 m/s Train velocity is +10 m s−1+10\,\mathrm{m\,s^{-1}} Train velocity is 00
Seat fixed inside the train Seat changes ground position Seat position is constant

Changing frames can change the measured position and velocity—both magnitude and direction—but does not change the underlying event. State conclusions as ‘relative to the ground’ or ‘relative to the train.’

Use the inertial-frame assumption

Different frame-dependent values are not contradictory. Unless a problem says otherwise, AP Physics 1 lets you assume the reference frame is inertial: it is not accelerating or rotating relative to another inertial frame.