Reference Frames
Summary
TLDRThis 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
- ๐ Reference frames are essential for discussing an object's motion, as they provide a point of comparison for velocity or movement.
- ๐ The ground is commonly used as a default reference frame when one is not specified.
- ๐ An object's velocity is always relative to its chosen reference frame, which could be another moving object.
- ๐ Velocity can be positive or negative depending on the direction relative to the reference frame.
- ๐ถโโ๏ธ 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.
- ๐ถโโ๏ธ 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.
- ๐ค The relative velocity between two objects can be determined by subtracting their velocities with respect to the ground.
- ๐งฎ 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.
- ๐ When calculating velocities, it's crucial to consider the direction of movement and whether to add or subtract the values.
- ๐ 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
๐ 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.
๐ 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.
๐ 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.
Mindmap
Keywords
๐กReference Frames
๐กVelocity
๐กRelative Motion
๐กUnits of Velocity
๐กPositive and Negative Velocities
๐กVelocity Calculations
๐กTrain Example
๐กEast and West Directions
๐กObserver's Perspective
๐กCommon Reference Frame
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
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