Reference Frames & Relative Motion (College Board AP® Physics 1: Algebra-Based)

Study Guide

Test yourself

Author

Leander Oates

Expertise

Physics

Reference frames & relative motion

A reference frame, or frame of reference is defined as:

A coordinate system in which an observer makes position and time measurements of physical events

All objects in the universe are moving relative to each other
For example, a person sitting at a desk may describe themselves as stationary; however, planet Earth is currently:
- rotating on its axis at 1600 kilometers per hour
- orbiting the Sun at 107 000 kilometers per hour
Therefore, measurements like position and velocity can be different depending on the reference frame from which they are measured

Direction in reference frames

The direction of motion of an object can be different in different reference frames
For example, a car is driving down a road and two people are standing on opposite sides of that road
- The person on one side of the road would say the car is moving to the right, and the person on the other side of the road would say the car is moving to the left
- Both are correct, but they are viewing the car's motion from different frames of reference

Diagram showing different frames of reference for a moving car

Illustration shows a blue car on a road with a man saying "The car is travelling to the right" and a woman saying "The car is travelling to the left." — **One person measures the car to be moving to the left and another person measures the car to be moving to the right, based on their frame of reference**

Motion in reference frames

Motion itself can be relative, depending on the frame of reference
For example, a train passes through a station; Person A is on the platform and Person B is on the train
- Person A, on the platform, views Person B, on the train, moving to the right
- According to Person A, they, themselves, are stationary and Person B is moving to the right
Things look a little different from Person B's perspective
- Person B, on the train, views Person A, on the platform, moving to the right
- According to Person B, they, themselves, are stationary and Person A is moving to the right

Different frames of reference for a train passing through a station

Diagram depicting relativity of motion: A person (A) stands on a platform, perceiving a train with person (B) inside moving right. B sees A moving right from their viewpoint. — **Person A and B are both stationary in their own reference frames and see the other as moving**

Converting measurements between reference frames

Measurements from a given reference frame may be converted to measurements from another reference frame
- Combining the motion of an object and the motion of an observer in a given reference frame involves the addition or subtraction of vectors

Position

The choice of reference frame will determine the direction and magnitude of quantities measured by an observer in that reference frame

At $t = 0$ a car is driving down a road with a constant velocity
Person A is 10 meters ahead of the car
Person B is 10 meters behind the car

Diagram showing a car between two points, A and B. The car is 10 meters from both points. Point A is marked with a blue dot and point B with a red dot. Time is t=0. — **At t = 0, Person A is 10 m in front of the car, Peron B is 10 m behind the car**

Taking the direction of motion of the car to be the positive direction:
- From the reference frame of Person A, the car is at position $x_{0} = - 10 m$
- From the reference frame of Person B, the car is at position $x_{0} = 10 m$
The car is traveling at $5 m / s$ , so at $t = 1 s$ the car has traveled $5 m$ in the positive direction

A diagram illustrating a car's movement. The orange car moves from point A, marked by a blue dot, to point B, marked by a red dot. Distances shown are -5m and 15m. Time is 1s. — **At t = 1 s, the car has traveled 5 m in the positive direction**

At $t = 1 s$ :
- From the reference frame of Person A, the new position of the car is $x = - 5 m$
- From the reference frame of Person B, the new position of the car is $x = 15 m$
The magnitude of the displacement of the car is the same in both reference frames

$∆ x = x - x_{0}$

$∆ x_{A} = (- 5) - (- 10) = - 5 m$

$∆ x_{B} = 15 - 10 = 5 m$

The direction in which the car has moved is relative to the frame of reference

Velocity

The observed velocity of an object results from the combination of the object’s velocity and the velocity of the observer’s reference frame

At $t = 2 s$ , the car passes Person A, and a truck with a velocity of $10 m / s$ over takes the car

At time t = 2 seconds, a blue truck moves at 10 m/s, an orange car at 5 m/s, and a blue dot labeled A is stationary with a velocity of 0. — **At t = 2 s, the car passes Person A and a truck overtakes the car**

From Person A's reference frame:
- Person A is stationary, ${\vec{v}}_{A} = 0$
- Person A measures the velocity of the car to be, ${\vec{v}}_{c a r} = 5 m / s$
- Person A measured the velocity of the truck to be, ${\vec{v}}_{t r u c k} = 10 m / s$
From the car's reference frame:
- The car is stationary, ${\vec{v}}_{c a r} = 5 - 5 = 0 m / s$
- The car measures Person A moving away in the negative direction with a velocity, ${\vec{v}}_{A} = 0 - 5 = - 5 m / s$
- The car measures the truck moving away in the forward direction with a velocity, ${\vec{v}}_{t r u c k} = 10 - 5 = 5 m / s$
From the truck's reference frame:
- The truck is stationary, ${\vec{v}}_{t r u c k} = 10 - 10 = 0 m / s$
- The truck measures Person A moving away in the negative direction with a velocity, ${\vec{v}}_{A} = 0 - 10 = - 10 m / s$
- The truck measures the car moving away in the negative direction with a velocity, ${\vec{v}}_{c a r} = 5 - 10 = - 5 m / s$

Inertial reference frames

An inertial reference frame is a nonaccelerating reference frame
- Inertial reference frames move at a constant velocity
A person in a moving vehicle that is traveling at a constant velocity cannot feel that they are moving
- For example, when on an airplane, once it has reached cruising altitude
A person in a moving vehicle that is accelerating can feel that they are moving
- For example, when on an airplane during take off and landing
Therefore, within an inertial reference frame, a person cannot feel that they are moving; they consider themselves to be stationary
The acceleration of any object is the same as measured from all inertial reference frames
- Inertial reference frames are covered in more detail in the study guide on Newton's first law

Examiner Tip

In AP Physics 1, you will only need to consider inertial reference frames when converting measurements.

You've read 0 of your 10 free study guides

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Test yourself Next topic

Did this page help you?