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Determine all the following: 1. Write an expression for the upper limit of the integral: Upper Limit =        2. Write an expression for r: r =  x       3. The formula for Moment of Inertia in the form of an integral: I = ∫  r2·dm       4. Write the result for the Moment of Inertia: I =

Determine all the following: 1. Write an expression for the upper limit of the integral: Upper Limit =        2. Write an expression for r: r =  x       3. The formula for Moment of Inertia in the form of an integral: I = ∫  r2·dm       4. Write the result for the Moment of Inertia: I =

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I only need help with number 1 and 4.
President Teddy Roosevelt's most famous saying was Walk softly, but carry a big stick. He and this saying were immortalized in many ways including the cartoon shown below. Even though the stick in the picture does not look like the mass is uniformly distributed along the length, we shall treat it as such. The stick is made of Mahogany and has been painted with blue paint so that the president's rivals can see it and quake in fear. Teddy grips the stick at the point 17% from the bottom edge using a normal force between his hands and the stick of 30 Newtons. It is a warm day outside 102 degrees Fahrenheit and profuse sweating has lower the coefficient of static friction to 0.35 between the hands and the stick. The stick of Mass M and length L is swung with an angular velocity of 1.7 rad/second counter-clockwise as viewed from above. Nearby a lark sings with a note whose frequency is 190 Hz.


Determine all the following:
1. Write an expression for the upper limit of the integral: Upper Limit = 
 
 
 

2. Write an expression for r: r = 
x
 
 
 
3. The formula for Moment of Inertia in the form of an integral: I = ∫ 
r2·dm
 
 
 
4. Write the result for the Moment of Inertia: I = 
 
 
 
 .
5. Write an expression for dm: dm = 
ML​·dx
 
 
 
6. Write an expression for the lower limit of the integral: Lower Limit = 
−.17·L
 
 
 


NOTE:
  • Don't enter limits for the integral formula, just supply the integrand.
  • Be careful with signs.
  • Be careful with capitalization.
  • Use at least 3 decimal places for the number in Moment of Inertia formula.
 
 
### Transcription and Explanation for Educational Use #### Image Description The image consists of two main parts: an illustration of a man holding a large club and a diagram featuring a labeled bar. #### Illustration Details - The illustration on the left depicts a man wielding a club. The club is divided into two sections: "short" and "long," labeled in red. - The man stands surrounded by what appears to be oil barrels and rubble. #### Diagram Details - The diagram on the right shows a horizontal bar divided into two segments, labeled as "short" and "long," mirroring the divisions in the club illustration. - The bar is colored yellow and is positioned along the x-axis, with the length denoted as "L." - Both ends of the bar have curly braces showing the "short" and "long" sections. - The Cartesian coordinate system is visible with both x and y axes. The x-axis is horizontal, highlighting the length of the bar. - A right arrow along the x-axis and a vertical line represent the coordinate system's directions. ### Educational Context This image can be used to explain concepts of proportions, measurement, and visualization in physics or mathematics. The division of the club into "short" and "long" sections emphasizes proportionality, which is mirrored in the labeled bar in the diagram. This analogy might be useful to understand the breakdown of a total length (L) into distinct parts and how such concepts can be visualized mathematically or physically.
Transcribed Image Text:### Transcription and Explanation for Educational Use #### Image Description The image consists of two main parts: an illustration of a man holding a large club and a diagram featuring a labeled bar. #### Illustration Details - The illustration on the left depicts a man wielding a club. The club is divided into two sections: "short" and "long," labeled in red. - The man stands surrounded by what appears to be oil barrels and rubble. #### Diagram Details - The diagram on the right shows a horizontal bar divided into two segments, labeled as "short" and "long," mirroring the divisions in the club illustration. - The bar is colored yellow and is positioned along the x-axis, with the length denoted as "L." - Both ends of the bar have curly braces showing the "short" and "long" sections. - The Cartesian coordinate system is visible with both x and y axes. The x-axis is horizontal, highlighting the length of the bar. - A right arrow along the x-axis and a vertical line represent the coordinate system's directions. ### Educational Context This image can be used to explain concepts of proportions, measurement, and visualization in physics or mathematics. The division of the club into "short" and "long" sections emphasizes proportionality, which is mirrored in the labeled bar in the diagram. This analogy might be useful to understand the breakdown of a total length (L) into distinct parts and how such concepts can be visualized mathematically or physically.
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