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A circular rim 28 inches in diameter rotates the same number

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A circular rim 28 inches in diameter rotates the same number [#permalink] New post 29 Jul 2003, 14:32
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A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim make in terms of x?
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 [#permalink] New post 29 Jul 2003, 20:26
Linear velocities of the points lying on both circles are the same.

Linear velocity=Angle velocity*Radius

X*14=Y35/2

Y=2*14*X/35 revolutions per second; it will rotate 60 times the number per minute

Y=2*14*60*X/35=48X
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 [#permalink] New post 29 Jul 2003, 22:54
stolyar wrote:
Linear velocities of the points lying on both circles are the same.

Linear velocity=Angle velocity*Radius

X*14=Y35/2

Y=2*14*X/35 revolutions per second; it will rotate 60 times the number per minute

Y=2*14*60*X/35=48X


Stolyar:

You are very analytical, but you need to do "sanity checks" on your answers. One circle is merely 20% larger than the other in scale. What makes you think that it is possible for one to rotate 48 times as fast as the other?

The answer that doesn't make any physical sense is usually wrong....

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AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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 [#permalink] New post 30 Jul 2003, 02:23
AkamaiBrah wrote:
stolyar wrote:
Linear velocities of the points lying on both circles are the same.

Linear velocity=Angle velocity*Radius

X*14=Y35/2

Y=2*14*X/35 revolutions per second; it will rotate 60 times the number per minute

Y=2*14*60*X/35=48X


Stolyar:

You are very analytical, but you need to do "sanity checks" on your answers. One circle is merely 20% larger than the other in scale. What makes you think that it is possible for one to rotate 48 times as fast as the other?

The answer that doesn't make any physical sense is usually wrong....


Akamai,

You forget that Y=48x is in revolutions per minute whereas x is in revolutions per second !!

If we use the same units, revolutions per second, then the larger circle's angular speed is (28/35)x=0.8x
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 [#permalink] New post 30 Jul 2003, 02:52
I think it should equal to X*28/35.

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 [#permalink] New post 30 Jul 2003, 03:05
hopeful wrote:
I think it should equal to X*28/35.

Regards,

Hopeful


Hopeful,

The questions clearly asks for the answer in revolutions per minute
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 [#permalink] New post 30 Jul 2003, 04:03
you are right! it shoud be X*60*28/35=48X

Thank you,

Hopeful
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 [#permalink] New post 30 Jul 2003, 05:15
AkamaiBrah wrote:
stolyar wrote:
Linear velocities of the points lying on both circles are the same.

Linear velocity=Angle velocity*Radius

X*14=Y35/2

Y=2*14*X/35 revolutions per second; it will rotate 60 times the number per minute

Y=2*14*60*X/35=48X


Stolyar:

You are very analytical, but you need to do "sanity checks" on your answers. One circle is merely 20% larger than the other in scale. What makes you think that it is possible for one to rotate 48 times as fast as the other?

The answer that doesn't make any physical sense is usually wrong....


The question does not require to understand the physical sense directly. It uses different measures -- minutes and seconds. So, sanity cheking tells that the bigger circle rotates at X28/35 rps, a smaller rate that that of the first small circle (X rps). It is OK. But we have to translate the rate into rpm by multiplying it by 60.
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 [#permalink] New post 30 Jul 2003, 05:50
prashant wrote:
AkamaiBrah wrote:
stolyar wrote:
Linear velocities of the points lying on both circles are the same.

Linear velocity=Angle velocity*Radius

X*14=Y35/2

Y=2*14*X/35 revolutions per second; it will rotate 60 times the number per minute

Y=2*14*60*X/35=48X


Stolyar:

You are very analytical, but you need to do "sanity checks" on your answers. One circle is merely 20% larger than the other in scale. What makes you think that it is possible for one to rotate 48 times as fast as the other?

The answer that doesn't make any physical sense is usually wrong....


Akamai,

You forget that Y=48x is in revolutions per minute whereas x is in revolutions per second !!

If we use the same units, revolutions per second, then the larger circle's angular speed is (28/35)x=0.8x


Ahh. my bad. Apologies to Stolyar (although you still need to use sanity checks!).

_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

  [#permalink] 30 Jul 2003, 05:50
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