Dimentional Anaylsis: Solving for Revolutions

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In summary, the NASA Cassini mission released a probe named Huygens to land on Saturn's moon Titan on December 25, 2004. It rotated at a rate of 7 revolutions per minute while moving away from the main spacecraft, and had completed 55 revolutions when it was 160 yards away.
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valerieangel
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NASA's Cassini mission to Saturn released a probe on December 25, 2004, that landed on the Saturnian moon Titan on January 14, 2005. The probe, which was named Huygens, was released with a gentle relative speed of 31 cm/s. As Huygens moved away from the main spacecraft , it rotated at a rate of seven revolutions per minute.

How many revolutions had Huygens completed when it was 160 yards from the mother ship?


I know the answer is 55 rev; however, I got a completely different answer. I solved for the answer this way:

160yd*(3ft/yd)*(12in/ft)*(2.54cm/in) = x

I then divided x by 31 cm/s, and multiplied it by 420 rev/s.


Any help or advice would be much appreciated. :smile:
 
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How can something that does only 7 revolutions in 60 seconds do 420 revolutions in 1 second?
 
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Muphrid said:
How can something that does only 7 revolutions in 60 seconds do 420 revolutions in 1 second?

You're right. I don't know what I was thinking! I did figure out that I needed to divide 7rpm by 60s and multiply that number by 471.948s, which gave to 55rev. :smile:
 

1. What is dimensional analysis?

Dimensional analysis is a mathematical technique used to convert between different units of measurement. It involves using conversion factors and algebraic equations to solve for unknown quantities.

2. How is dimensional analysis useful in solving for revolutions?

In rotational motion, revolutions are a common unit of measurement for angular displacement. Dimensional analysis allows us to convert between different units of angular displacement, such as degrees, radians, and revolutions, to solve for unknown quantities related to rotational motion.

3. What are the steps for using dimensional analysis to solve for revolutions?

The steps for using dimensional analysis to solve for revolutions are as follows:

  1. Identify the given quantity and the desired quantity, both expressed in different units of angular displacement.
  2. Write down the conversion factors for converting between the given and desired units.
  3. Set up an algebraic equation using the given quantity, the desired quantity, and the conversion factors.
  4. Solve the equation to find the desired quantity in terms of revolutions.

4. Can dimensional analysis be used for other types of motion besides rotations?

Yes, dimensional analysis can be used for any type of motion as long as there are units of measurement involved. It is commonly used in physics and engineering to convert between units of length, time, velocity, acceleration, and more.

5. Are there any limitations to using dimensional analysis for solving for revolutions?

Yes, dimensional analysis assumes that the physical quantity being measured is proportional to the units of measurement. This may not always hold true, especially for complex systems with nonlinear relationships between quantities. In these cases, other methods may be necessary for solving for revolutions.

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