Unit when multiplied or squared

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When multiplying units like (5 lbs•m^2) and (5 rad/s^2) by 2, the units remain unchanged; they still represent the same physical quantities. Squaring these units results in (5 lbs^2•m^4) for (a) and (5 rad^2/s^4) for (b). The discussion highlights the importance of clarity in unit representation, particularly with mixed measurement systems. Additionally, it emphasizes the need to differentiate between squaring a unit and multiplying it by a constant. Overall, understanding how units transform under multiplication and squaring is crucial in physics.
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Homework Statement



Consider the following hypothetical question:

(5 lbs•m^2) =a
(5 rad/s^2) =b

If (a) and (b) are each multiplied by 2 what do the units become?

Similarly if (a) and (b) are squared what do the units become ?
 
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K.Callaghan said:

Homework Statement



Consider the following hypothetical question:

(5 lbs•m^2) =a
(5 rad/s^2) =b

If (a) and (b) are each multiplied by 2 what do the units become?

Similarly if (a) and (b) are squared what do the units become ?
If you have a square which measures one meter on a side, what is the length of the sides of the square if you double that distance?

If a square measures 1 meter on a side, what is the area of the square? If a cube measures 1 meter on a side, what is its volume?

BTW, its not clear what kind of unit the lbs-m2 is. Is that supposed to be "pounds-mass" or "pounds-meter"?

Generally, it's not cool to use a mixture of units from different measurement systems.
 
SteamKing said:
If you have a square which measures one meter on a side, what is the length of the sides of the square if you double that distance?

If a square measures 1 meter on a side, what is the area of the square? If a cube measures 1 meter on a side, what is its volume?

BTW, its not clear what kind of unit the lbs-m2 is. Is that supposed to be "pounds-mass" or "pounds-meter"?

Generally, it's not cool to use a mixture of units from different measurement systems.

Thanks for your reply! I don't think I was specific enough here, My question worded differently would be ;

if Mass^2 = kg^2

What would (mass^2 multiplied by 2)
= in its units?

Do the units change or remain the same.
I know this is a very silly question!
 
K.Callaghan said:
Thanks for your reply! I don't think I was specific enough here, My question worded differently would be ;

if Mass^2 = kg^2

What would (mass^2 multiplied by 2)
= in its units?
Are you talking about squaring units of mass2, or are you talking about multiplication of units of mass2 by a constant value (for example, 2)?

Either way, the answer should be self-evident.
 
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K.Callaghan said:

Homework Statement



Consider the following hypothetical question:

(5 lbs•m^2) =a
(5 rad/s^2) =b

If (a) and (b) are each multiplied by 2 what do the units become?

Similarly if (a) and (b) are squared what do the units become ?
Where is your attempt at solving this yourself?
 
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