Reference Frames

Summary

This video script delves into the concept of reference frames in physics, crucial for describing an object's motion. It explains that velocity is always relative to something, the reference frame. Using examples of John and Sally, it illustrates how to calculate velocities relative to the ground and to each other. The script also covers scenarios on a moving train, showing how to determine velocities using formulas and a common reference frame, emphasizing the importance of understanding reference frames in motion analysis.

Takeaways

• 📏 Reference frames are essential for discussing an object's motion, as they provide a point of comparison for velocity or movement.
• 🌐 The ground is commonly used as a default reference frame when one is not specified.
• 🚀 An object's velocity is always relative to its chosen reference frame, which could be another moving object.
• 🔄 Velocity can be positive or negative depending on the direction relative to the reference frame.
• 🚶‍♂️ John's velocity relative to the ground is calculated by adding his walking speed to the train's speed if they are moving in the same direction.
• 🚶‍♀️ Sally's velocity relative to the ground is found by adding her walking speed to the train's speed, considering her direction is opposite to the train's.
• 🤔 The relative velocity between two objects can be determined by subtracting their velocities with respect to the ground.
• 🧮 The formula for relative velocity is V(AB) = V(A) - V(B), where V(AB) is the velocity of object A relative to object B.
• 🚄 When calculating velocities, it's crucial to consider the direction of movement and whether to add or subtract the values.
• 🔄 Changing reference frames can provide different perspectives on the same motion, but the mathematical relationships remain consistent.

Q & A

Why are reference frames important in discussing motion?

Reference frames are important because they provide a point of comparison when discussing an object's motion, such as its velocity. They allow us to describe how fast an object is moving relative to something else, which is necessary for understanding motion.

What is the default reference frame when one is not specified?

When a reference frame is not specified, it is typically assumed to be the ground.

How does the velocity of an object change when described relative to different reference frames?

The velocity of an object can appear different when described relative to different reference frames. For example, a car moving at 20 meters per second relative to a bus might have a different velocity when described relative to the ground.

What is the relationship between John's velocity and Sally's velocity when both are moving relative to the ground?

When John is moving at 2 miles per hour and Sally is moving at 3 miles per hour relative to the ground, Sally's velocity relative to John (v_s_j) is 1 mile per hour, as she is moving faster than John.

How can you calculate the velocity of one object relative to another using a formula?

The velocity of one object relative to another can be calculated using the formula: V_object1_relative_to_object2 = V_object1_relative_to_ground - V_object2_relative_to_ground.

What is the significance of a negative velocity in the context of reference frames?

A negative velocity indicates that an object is moving in the opposite direction relative to the reference frame. For example, if Sally is moving west while the train is moving east, her velocity relative to the train would be negative.

How does the motion of a train affect the velocities of people walking on it relative to the ground?

The velocities of people walking on a moving train relative to the ground are the sum of their velocities relative to the train and the train's velocity relative to the ground, depending on whether they are walking in the same or opposite direction as the train.

What is the formula to calculate an object's velocity relative to the ground when it is moving on a vehicle?

The formula to calculate an object's velocity relative to the ground when it is on a moving vehicle is: V_object_ground = V_object_vehicle + V_vehicle_ground.

Why does the reference frame chosen affect the perceived velocity of an object?

The reference frame chosen affects the perceived velocity of an object because it determines what the object is being compared against. Different reference frames can yield different velocities for the same object.

How can you determine the velocity of one person relative to another when both are moving on a train?

To determine the velocity of one person relative to another on a train, you can use the formula: V_person1_relative_to_person2 = V_person1_ground - V_person2_ground, using the ground as a common reference frame.

Outlines

00:00

🚀 Understanding Reference Frames

This paragraph introduces the concept of reference frames in the context of describing an object's motion. It explains that velocity is always relative to something, which is the reference frame. Examples are given to illustrate how different reference frames can change the perception of an object's motion. The paragraph uses the example of an airplane moving relative to the ground and a car moving relative to a bus to demonstrate the importance of reference frames. It then introduces the scenario of two people, John and Sally, moving at different speeds relative to the ground, and discusses how their velocities change when viewed from different reference frames.

05:02

🔍 Calculating Velocities with Reference Frames

This paragraph delves into the mathematical aspect of calculating velocities relative to different reference frames. It uses the example of John and Sally moving at different speeds and explains how to determine their velocities relative to each other. The paragraph provides a formula for calculating the velocity of one object relative to another by subtracting their velocities relative to the ground. It also presents an example problem involving John and Sally on a moving train, walking in different directions, and explains how to calculate their velocities relative to the ground and to each other using the same principles.

10:04

🚆 Applying Reference Frames to a Train Scenario

The final paragraph extends the concept of reference frames to a more complex scenario involving a train moving at a constant speed with John and Sally walking in opposite directions on it. It describes how to calculate John's and Sally's velocities relative to the ground by considering the train's velocity and their walking speeds. The paragraph also discusses how to determine their velocities relative to each other using both the ground and the train as reference frames. It concludes by emphasizing the importance of reference frames in accurately describing motion and velocity.

Keywords

💡Reference Frames

Reference frames are the basis for describing motion. They are the points of reference against which the motion of an object is measured. In the video, the importance of reference frames is emphasized as they are essential for discussing an object's velocity. For instance, an airplane's speed is described relative to the ground, making the ground the reference frame. The concept is central to understanding how motion is relative and depends on the chosen frame of reference.

💡Velocity

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time, in a specific direction. The video uses velocity to illustrate the need for reference frames. It explains that velocity is always relative to something, like the ground or another moving object, and provides examples such as a car moving relative to a bus, where the bus acts as the reference frame.

💡Relative Motion

Relative motion refers to how the position or velocity of an object is observed to change with respect to another object. The video script uses the example of a person named John moving relative to the ground and another person named Sally moving relative to John to explain how velocities add or subtract depending on the direction of motion. This concept is crucial for understanding how motion is perceived differently by different observers.

💡Units of Velocity

Units of velocity, such as meters per second or miles per hour, are used to quantify how fast an object is moving. In the video, the script changes the units of John's velocity from meters per second to miles per hour to make it more relatable. Understanding these units is important for comparing velocities and performing calculations involving motion.

💡Positive and Negative Velocities

The video discusses the concept of positive and negative velocities to indicate direction. A positive velocity indicates motion in one direction (e.g., to the right), while a negative velocity indicates motion in the opposite direction (e.g., to the left). This is demonstrated when calculating John's velocity relative to Sally, where John's velocity is positive because he is moving in the same direction as the chosen reference frame.

💡Velocity Calculations

The video provides formulas and examples for calculating velocities relative to different reference frames. It shows how to determine an object's velocity with respect to another object by subtracting velocities. For example, Sally's velocity relative to John is calculated by subtracting John's velocity from Sally's velocity, demonstrating how to apply mathematical operations to determine relative motion.

💡Train Example

The train example in the video script is used to illustrate complex scenarios involving multiple reference frames. It describes a scenario where John and Sally are on a moving train, with each walking in different directions relative to the train. This example helps to understand how velocities combine when objects are moving relative to each other and to a third reference frame, such as the ground.

💡East and West Directions

The video uses the terms 'East' and 'West' to denote the direction of motion. These directional terms are crucial for understanding the relative velocities of objects. For instance, John walking east at a certain speed and Sally walking west at a different speed on a train moving east help to calculate their velocities relative to the ground and to each other.

💡Observer's Perspective

The video mentions the perspective of an observer standing on the ground, which is important for understanding how different reference frames can lead to different observations of the same motion. The observer's perspective is used to explain how John and Sally's velocities appear from the ground, which is different from their velocities relative to the train or each other.

💡Common Reference Frame

A common reference frame is necessary for comparing velocities between two objects. The video explains that while the ground can be a common reference frame, in some cases, like when both John and Sally are on the train, the train itself can serve as a common reference frame. This concept is important for simplifying calculations and understanding how relative velocities are determined.

Highlights

Reference frames are essential for discussing an object's motion.

Velocity is always relative to a reference frame.

An airplane's velocity is measured relative to the ground.

A car's velocity can be described relative to a bus.

The ground is typically the default reference frame if not specified.

John's velocity is 2 meters per second relative to the ground.

Changing units to miles per hour for a more relatable velocity measure.

Sally's velocity is 3 miles per hour relative to the ground.

Sally's velocity relative to John is 1 mile per hour.

John's velocity relative to Sally is -1 mile per hour.

The formula to calculate relative velocity is V_rel = V1 - V2.

John's velocity relative to the ground on a moving train is calculated.

Sally's velocity relative to the ground is found using the train as a reference.

John's velocity relative to Sally is 7 miles per hour.

Sally's velocity relative to John is -7 miles per hour.

Using a common reference frame like the train simplifies velocity calculations.

Reference frames are crucial for accurately describing motion and velocity.

Transcripts

in this video we're going to talk about

reference frames now you might be

wondering why are reference frames

important

well whenever you're discussing an

object's motion let's say it's velocity

you need to compare its velocity to

something you need to speak about its

velocity with respect to something and

that's something is the reference frame

for example you can say that an airplane

is moving at

200 meters per second relative to the

ground in this case the ground would be

the reference frame

you could say that a car is moving 20

meters per second relative to a bus

in that case the bus will be the

reference frame

what that means is that the car is

moving faster than the bus but you don't

really know the car speed relative to

the ground

so whenever you're talking about an

object's motion you need to compare it

with something and that something is the

reference frame

so let's look at some examples

let's say we have a person

we'll call this person

John

is moving at a speed of 2 meters per

second to the right

so his velocity is positive too

now what's the reference frame in this

example

if the reference frame is not specified

it's typically assumed to be the ground

in this case it is John is moving two

meters per second relative to the ground

so the ground is the reference frame

now I'm going to change the units of his

velocity because to move at a speed of 2

meters per second

that's actually quite fast for a person

so let's say it's two miles per hour

now we're going to have another person

we'll call this person

Sally

and let's say that's Sally is moving

at a velocity of 3 miles per hour

towards the right

and that's relative to the ground

so we'll call this V

J G

that is

John's velocity relative to the ground

and we'll call this v s g

Sally's velocity with respect to the

ground

and there's a question for you what

would be

the value of v s j

what is Sally's velocity

relative to John

well Sally is moving faster than John

from John's perspective

every hour Sally is going to be one mile

ahead of him

she's moving one mile per hour faster

than he is so the distance between John

and Sally will continually to increase

from John's perspective sadly is moving

away from him

so sadly

her speed is one mile per hour

greater than John

now we can also say what is John's

velocity relative to Sally

well John is moving slower than Sally

from Sally's perspective it appears as

if John is moving away from her

because she's moving ahead of him

so his velocity relative to her is

actually going to be negative one

miles per hour

so in this case for this value

the reference frame is John because

we're looking at sadly's velocity

relative to John

and for this value the reference frame

is Sally because we're looking at John's

velocity

with respect to Sally's

now for those of you who like to have

formulas

here's how you can

get the answer using the formula

the velocity of John relative to Sally

is basically the difference between the

two

it's John's velocity relative to the

ground minus Sally's velocity relative

to the ground

so VJs is going to be v j minus vs but

both with respect to the ground

and it makes sense if we plug in the

numbers 2 minus positive 3

will give us negative 1.

likewise

calculate Sally's velocity

relative to John it's going to be vs

minus v j

but Sally's velocity relative to the

ground minus John's velocity relative to

the ground

so vsj is 3 minus v j g which is

positive 2 and that gives us positive

one

so that's the math behind

the operations that gave us these two

answers

now let's work on an example problem

Sally and John are on a train that is

moving East at 50 miles per hour

relative to the ground

John is walking East at three miles per

hour and Sally is walking West at four

miles per hour

what is John's velocity with respect to

the ground

so let's draw a picture

so that's going to be the ground

and

let's draw a picture of a train

now on this train we see that John

John is walking East

at

3 meters per second

so we could say that

John's velocity relative to the train

is positive three

meters per second or rather miles per

hour

let's fix that

but what is his velocity relative to the

ground

so an observer who is standing on the

ground what does he see

an observer standing from the ground

he sees the train moving at 50 miles per

hour to the right relative to him

now in addition to that John is walking

to the right

he's walking three miles per hour faster

than a train so John's velocity

with respect to the ground as viewed by

an observer is actually going to be

positive

53 miles per hour it's going to be the

sum of the train and velocity because

they're both moving in the same

direction

now for those of you who like to use a

formula

to see the calculations here's what you

can do

John's velocity with respect to the

train is going to be

or in other words vjt is going to be VJ

with respect to the ground minus the VT

with respect to the ground

so vjt John's velocity with respects to

the train that's positive three

we're looking for John's velocity with

respect to the ground

and the Train's velocity with respect to

the ground we know it's positive 50.

so what we have is 3 equals v j g minus

50. well to get this answer we need to

add 50 to both sides

so moving negative 50 to the other side

it's going to be positive 50. minus I

mean Plus 3.

and that's how we get

vjg is positive 53.

so that's how you can use the formula to

get that answer

now let's move on to Part B what is

Sally's velocity with respects to the

ground

so sadly

is moving West

at four miles per hour and it says while

she's on the train

so Sally's velocity with respect to the

train is negative 4 miles per hour it's

negative because

she's moving to the left

now what is her velocity with respect to

the ground

well we could use the same formula

or something similar to it so VST is

going to be vs with respects to the

ground minus the VT with respect to the

ground

VST is negative four

v s g is what we're looking for

and the velocity of the train with

respect to the ground is negative 50.

so we need to add 50 to both sides so

it's going to be negative 4 plus 50.

and that's going to equal vsg

negative 4 plus 50 that's going to be

positive

46.

so to an observer on the ground

John is moving East

so John will appear to be moving faster

than the train

Sally's moving West so to an observer on

the ground Sally is going to be moving

slower

than the train she's still moving to the

right with respect to the Observer but

she's moving at a slower rate relative

to the train

now let's move on to part C

what is John's velocity with respect to

Sally

so we're looking for

v j s John's velocity with respect to

Sally

using the formula it's going to be

John's velocity with respect to the

ground minus

Sally's velocity with respect to the

ground

and we have those numbers

it's those two numbers so it's going to

be 53 minus positive 46

53 minus 46 that's positive 7.

so John's velocity relative to Sally

is positive 7.

what that means is that his velocity

is seven units to greater than Sally's

velocity which makes sense positive

three is seven more units than negative

four

now we can also get the same answer

using this formula

instead of

using the ground

as the common reference frame we can use

the train as a common reference frame

because both John and Sally are on a

train

so VJs can also be calculated used in

this formula vjt minus VST it works the

same as long as we use a common

reference frame

so vjt

that's positive 3.

minus v s t which is negative four

three minus negative 4 is the same as 3

plus 4. and it gives us

positive seven miles per hour

so that is John's velocity with respect

to solid

now what is Sally's velocity with

respect to John

all you got to do is switch to sine

so v j s is going to equal negative vsj

so that means it's going to be negative

seven miles per hour

and of course we could use the formula

VJs is going to be

I mean vsj

is going to be vs with respect to the

ground minus V J with respects to the

ground

so vsg is 46 minus vjg which is 53. and

that will give us negative seven miles

per hour

so that's Sally's velocity with respect

to John's

and that's basically it for this video

hopefully it gave you a good idea into

the concept of reference frames so

whenever you describe an object's motion

its velocity

you need to describe it

with respect to something and that

something is the reference frame