Linear Speed and Angular Velocity
ฝัง
- เผยแพร่เมื่อ 30 ก.ย. 2024
- This trigonometry video tutorial provides a basic introduction into linear speed and angular velocity. It discusses how to convert linear speed to angular speed. It explains how to convert rpm values or revolutions per minute into feet per second. It also shows you how to convert rad/s to m/s, rev/s to mph, km/hr to rpm, and miles per hour to radians per second. This video contains plenty of examples and practice problems.
Trigonometry - Basic Introduction:
• Trigonometry
Introduction to Angles:
• Introduction to Angles
Radians and Degrees:
• Radians and Degrees
What Exactly Is a Radian?
• Trigonometry - What Ex...
Coterminal Angles:
• Coterminal Angles In R...
_________________________
Decimal Degrees to DMS:
• Decimal Degrees to DMS...
Arc Length of a Circle and Sector Area:
• Arc Length of a Circle...
Linear Speed and Angular Velocity:
• Linear Speed and Angul...
Clock to Angle Problems:
• Clock Aptitude Reasoni...
The Unit Circle:
• The Unit Circle, Basic...
_______________________________________
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Final tomorrow. Anyone else?
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Me haha
lol yes
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right as I'm starting to get it, in comes a damn obnoxious car commercial with it's volume up about a trillion times louder than your voice.
LMAO
I was watching this before taking a quiz I thought I was set for
I am not.
Me right now lol
Dude you lost me at problem 2
Lul, same
lol same. What I got is 0.2060468. I calculate it 3 times.
Same
I suppose it's helpful to try to think what you have and what you need to get to. So angular speed is always radians/time and if you have radians you can convert directly to some measure of length/time.
MR. Organic Chemistry Tutor, thank you for another awesome video on Linear Speed and Angular Velocity.
Man I was on the struggle bus all day trying to understand what you explained in 20min. Thank you!
boy do I hate physics
I am ashamed that I am simping at this point..
This was actually so helpful
Radius is the lower case of R: r, as the standard representation. Here R is used to represent radius, confusing! Especially here also talking about Radian, easily getting switched with Radius. So, to easy the presentation, it would be better to use 'r' to represent radius, and to use 'R' to represent radian.
In my class, R is used for radius and "rad" is used for radian
This video helped me more than you can possibly imagine
Thanks it really helped. Now i'm faster at solving this kinds of problems
This helped me understand greatly! I was really struggling to understand what my teacher was doing but this help make things so much clearly. Adding a radian to the denominator of each radius given for these type of word problems helped me so much. Thank you!
Many people wonder why radians do not appear when we have radians*meters (rad • m).
Here is an attempt at an explanation:
Let s denote the length of an arc of a circle whose radius measures r.
If the arc subtends an angle measuring β = n°, we can pose a rule of three:
360° _______ 2 • 𝜋 • r
n° _______ s
Then
s = (n° / 360°) • 2 • 𝜋 • r
If β = 180° (which means that n = 180, the number of degrees), then
s = (180° / 360°) • 2 • 𝜋 • r
The units "degrees" cancel out and the result is
s = (1 / 2) • 2 • 𝜋 • r
that is, half of the circumference 2 • 𝜋 • r
s = 𝜋 • r
If the arc subtends an angle measuring β = θ rad, we can pose a rule of three:
2 • 𝜋 rad _______ 2 • 𝜋 • r
θ rad _______ s
Then
s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r
If β = 𝜋 rad (which means that θ = 𝜋, the number of radians), then
s = (𝜋 rad / 2 • 𝜋 rad) • 2 • 𝜋 • r
The units "radians" cancel out and the result is
s = (1 / 2) • 2 • 𝜋 • r
that is, half of the circumference 2 • 𝜋 • r
s = 𝜋 • r
If we take the formula with the angles measured in radians, we can simplify
s = (θ rad / 2 • 𝜋 rad) • 2 • 𝜋 • r
s = θ • r
where θ denotes the "number of radians" (it does not have the unit "rad").
θ = β / (1 rad)
and θ is a dimensionless variable [rad/rad = 1].
However, many consider θ to denote the measure of the angle and for the example believe that
θ = 𝜋 rad
and radians*meter results in meters
rad • m = m
since, according to them, the radian is a dimensionless unit. This solves the problem of units for
them and, as it has served them for a long time, they see no need to change it. But the truth is
that the solution is simpler, what they have to take into account is the meaning of the variables
that appear in the formulas, i.e. θ is just the number of radians without the unit symbol rad.
Mathematics and Physics textbooks state that
s = θ • r
and then
θ = s / r
It seems that this formula leads to the error of believing that
1 rad = 1 m/m = 1
and that the radian is a dimensionless derived unit as it appears in the International System of Units (SI), when in reality
θ = 1 m/m = 1
and knowing θ the angle measures β = 1 rad.
In the formula
s = θ • r
the variable θ is a dimensionless variable, it is a number without units, it is the number of radians.
When confusing what θ represents in the formula, some mistakes are made in Physics in the units of certain quantities, such as angular speed.
My guess is that actually the angular speed ω is not measured in rad/s but in
(rad/rad) / s = 1/s = s^(-1).
At minute 1:38 you say that “angular speed it's basically the angle divided by the time, so it could be degrees per second... it could be radians per second which is more common and even the revolutions per minute which can be described as rpms”. That is not so, although it is what most of the scientific community believe. The error comes from thinking that in the formula
ω = θ / t
θ is in degrees, radians or revolution. In reality, θ represents the “number of radians” without units. If the angle is measured in degrees or revolutions, unit conversions must be made.
When at minute 2:37 you write the formula
v = R • ω
it is implicit the relation
s = θ • R
since when substituting in the formula
v = s / t
v = θ • R / t
v = R • ω.
But in the formula
s = θ • R
θ represents the “number of radians” without units.
I will write another comment showing how this formula is obtained and what the variables mean.
Then, at minute 3:29 you say that “it helps to think of the radius as being the length per unit radian”. Such a statement is false. This then allows you to cancel out the radians that would appear in the calculations if you leave the radius in units of length.
For example, in the exercise you do starting at minute 3:52 you use the formula
v = ω • R.
Substituting the quantities
v = (8 rad/s) • (5 cm/rad)
and cancel the radians you get
v = 40 cm/s
We all know that, in this case, the linear speed is in cm/s. In reality
ω = 8 (rad/rad)/s
ω = 8 (1/s)
R = 5 cm
v = [8 (1/s)] • (5 cm)
v = 40 cm/s
What most of the scientific community says is that the radian is a dimensionless unit and is omitted. The latter is not true either, but they rely on the International System of Units (SI) brochure, which states that the radian is a dimensionless derived unit.
Thank u so much. I understand your explanation better than my teacher's.
Just annoyed we need the rad to convert to radian from ex 5. I had it perfect until the rad to rev conversions. I just went right to rev assuming 1 rev was 1.4 ft. ... like a dunce.
Hello wouldn’t it be linear velocity & angular speed? Since the angular velocity wouldn’t make sense as its constantly changing direction
definitely not here right before a test
12:15 am I expected to solve for this without a calculator afterwards? if yes, how much time does it usually take? cause i literally can`t visualize myself making this multiplication/division in less than 7 minutes
Thank you so much! I get it now. I wish you were my trig/precalc instructor.
Wow i still don't get it
So i have a problem where im being told to find the linear velocity if the radius is 1.5 meters and its angular velocity is 2rev/1.5s.... how does that work?
you still need help or you figured it out?
Great video as always. Thank you!
Pag nakita nyo to exam namin bukas saturday class nakaka ewan etong school nato
Please make a video on Laplace Transform with topics :
Transforms of elementary functions , Inverse Transforms , properties of Laplace Transform , Convolutions , Transforms of periodic functions , unit step functions , shifting theorems , Solution of ODE using transform .
Yes Please!!!!
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Helped a bunch. Thanks man:)
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What is the linear velocity a man driving a car in 60 km in two hours?
I think it’d be 30 km/hr
A tire rim an inner of 15 inches and the distance between the rim to the outside diameter of a tire is 5.5 inches. To the nearest foot , how far does the tire travel when it makes 15 revolution. ...pls show your solution.
A wheel is rotating without slipping with a linear velocity V. What is the linear velocity of the rim of the wheel at the point surface of contact?
I think I’m in love with you
I love your videos and think you break down and explain very well but I am still lost.
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Hi I would just like to make some clarifications in number 2 problem. What I did is I converted the omega=30rpm to rad/s and what I got was simply πrad/s.
Next, I converted the 4cm to ft having me 1.3214ft.
Then from those two I multiplied them and what I got was 4.213ft/s.
Simply, I converted them separately then multiplied them to get my linear speed, how could we have different answer?
i think you forgot to multiply the denominator 100(60)=6000
On Laplace transform please .....it would be very helpful ....it is a request sir .
I am struggling to understand the whole conversion factors thing
thx i goot stuck in a topic
This is really really helpful,Thank you very much sir!
This channel is amazing. Makes me want to go back to uni / school...
Thank you for making cal easier to understand.
thx
This type of exercise solving is purely practical and got no sense of logic in it
henri hatija exactly
Pure gold my friend. Thank you!
Mate, Just came here to thank you. I'm a 7th grader and can already solve calculus and trig problems all thanks to you.
radians- a measurement for angles
-the radius and arc length/ intercepted line are the same for 1 radian 57.3°?
clockwise- negative
how to radian pi/180
₩-omega / angular speedcounter-clockwise- positive
radian to degree 180/pi
¤- theta / central angle-
coterminal- same ending 0
my memory is so bad 😭😭😭😭
i hate my memory 😭😭😭😭
wait for number 5 dont you have to divide 30.196 by 1.7...... help
I'm starting to like Math :)
I think for 2:01 i think that rpm is either for periods or frequencies.
A merry go round with a radius of 6.0 meters rotates at a speed of 8 revolutions per minute (rpm).
1. Calculate for the angular speed in rad/s
2. Find the tangential velocity of the merry go round
3. If the merry go round stops after one minute, what is its angular acceleration
helppp
Lol I’ll help you when I pass my test tomorrow, now I have to learn a whole chapter and do homework’s in less than nine hours. 4:18AM, 9/13/21.
@@yourmajestytheinternetuserthank you! i already answered it, i hope you pass your test
3:49 can someone explain why looking at 5cm as 5cm/radian makes sense
💀💀 because a radian divided by radian is 1.
くさんありますありがとうございます」、
THIS WAS SO HELPFUL THX FOR THE VIDEO
Thank you so much!
live saver in my GF's calc class
Thx for this hard problem
Nice and wonderful
The diameters of a pulley are 600mm and 1m respectively. When the system is released from rest, the mass descends with constant acceleration a distance of 3m during 20s. Calculate (a) the linear acceleration of each hanging mass;(b) the velocity of each hanging body 10s after being released; (c) the angular acceleration of the pulley and its angular velocity after 10s of movement
Please calculate this ome for me
please upload power system concepts videos and please continue that section.
Thanks this helped me understand better
Nice video! Do you also have an video about angular velocity to g force?
Is radians necessary for the angular velocity?
radians is a unit of angle. Just like how degrees is also a unit of angle. So yes, it is necessary to compute angular velocity.
16:58 i thought it was meters per hr
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How
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2:42 - What are the correct units here: ω = θ/t where θ is in angle, so ω is in the unit of angle/s. This makes V in the unit of meter x angle/s in V = rω (r=radius). So there seems too many units here (i.e. what is meter x angle?). V = S/t is easy to understand where S is length, hence V has the usual unit of meter/s.
Note that radius can also be interpreted as length/radians. If you multiply that with angular speed (radians/time) the radians cancel, so linear speed will become length/time.
yo i think prob 2 is wrong
I am thinking the same thing.
@Triple A OMG thank you for clarifying. He definitely forgot to mention x (3.14). I was seriously freaking out over here. You just saved my Final tomorrow.
Dimensional analysis (conversion of units) is awesome.
I have a test tomorrow and i now ill atleast get some points
OMGG! thank you so much on the conversion information! i didn't put my 2pi in parentheses and kept getting the wrong answer!!! thank you!