If I square a value units of radians, is the result in units of radians squared or is it still radians?
$begingroup$
I am writing a paper on circular motion. A function given is $$T=Msω^2L$$
The units for $ω$ are $text{rad}/s$. What are the units for $ω^2$? Are they $text{rad}^2/s^2$ or $text{rad}/s^2$? If they are the latter, why does $ω^2$ the units the same as those for angular acceleration?
physics mathematical-physics angle
edited Dec 5 '18 at 21:04
stafusa
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
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add a comment |
$begingroup$
I am writing a paper on circular motion. A function given is $$T=Msω^2L$$
The units for $ω$ are $text{rad}/s$. What are the units for $ω^2$? Are they $text{rad}^2/s^2$ or $text{rad}/s^2$? If they are the latter, why does $ω^2$ the units the same as those for angular acceleration?
physics mathematical-physics angle
edited Dec 5 '18 at 21:04
stafusa
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
$endgroup$
add a comment |
$begingroup$
I am writing a paper on circular motion. A function given is $$T=Msω^2L$$
The units for $ω$ are $text{rad}/s$. What are the units for $ω^2$? Are they $text{rad}^2/s^2$ or $text{rad}/s^2$? If they are the latter, why does $ω^2$ the units the same as those for angular acceleration?
physics mathematical-physics angle
edited Dec 5 '18 at 21:04
stafusa
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
$endgroup$
I am writing a paper on circular motion. A function given is $$T=Msω^2L$$
The units for $ω$ are $text{rad}/s$. What are the units for $ω^2$? Are they $text{rad}^2/s^2$ or $text{rad}/s^2$? If they are the latter, why does $ω^2$ the units the same as those for angular acceleration?
physics mathematical-physics angle
physics mathematical-physics angle
edited Dec 5 '18 at 21:04
stafusa
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
edited Dec 5 '18 at 21:04
stafusa
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
edited Dec 5 '18 at 21:04
stafusa
1227
edited Dec 5 '18 at 21:04
stafusa
1227
edited Dec 5 '18 at 21:04
stafusa
1227
1227
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
asked Dec 5 '18 at 14:45
Raymo111Raymo111
2107
2107
add a comment |
add a comment |
1 Answer
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$begingroup$
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $omega^2$ has units $1/s^2$.
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
$endgroup$
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
|
show 2 more comments
Your Answer
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1 Answer
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active
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1 Answer
1
active
oldest
votes
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active
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votes
$begingroup$
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $omega^2$ has units $1/s^2$.
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
$endgroup$
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
|
show 2 more comments
$begingroup$
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $omega^2$ has units $1/s^2$.
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
$endgroup$
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
|
show 2 more comments
$begingroup$
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $omega^2$ has units $1/s^2$.
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
$endgroup$
Radians are dimensionless, since they are defined as the ratio of arclength to radius when you look at what an angle cuts out of a circle. That ratio is length/length. So if $omega$ has units radians/second the dimensional analysis treats that as $1/s$. Then $omega^2$ has units $1/s^2$.
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
answered Dec 5 '18 at 14:52
Ethan BolkerEthan Bolker
42.4k549112
42.4k549112
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
|
show 2 more comments
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Can you explain the similarity between angular acceleration and angular velocity squared then?
$endgroup$
– Raymo111
Dec 5 '18 at 14:54
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Sorry, I can't help you there. That may be a good question for physics.stackexchange.com
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:56
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
Cool, thank you! I will accept your answer when the system allows me.
$endgroup$
– Raymo111
Dec 5 '18 at 14:57
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
If you get an answer there please let me know so I can learn something.
$endgroup$
– Ethan Bolker
Dec 5 '18 at 14:58
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
$begingroup$
I will post a link for you when I get an answer. Apparently I can only ask a question every 40 minutes.
$endgroup$
– Raymo111
Dec 5 '18 at 15:00
|
show 2 more comments
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