Help with Steps 1 & 2 of Math Problem

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To solve the math problem involving the U-shaped piece, it is essential to treat the structure as three separate rods with their respective centers of mass. The vertical rods are assumed to be 10 cm long, while the horizontal rod is 6 cm long. When calculating the moment of inertia, the vertical rods rotate about one end, whereas the horizontal rod should be treated as a point mass. This distinction is crucial for obtaining the correct answer. Understanding these points clarifies the approach needed for steps 1 and 2 of the problem.
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Hint: Treat the U-shaped piece as consisting of three thin rods. For calculating the center of mass, treat them as three separates masses (located at the centers of the three rods).
 
I have tried treating the U-shaped piece as consisting of three rods but this gives me:

Itotal= 2 I10 cm + I 6 cm =

2 (1/3) (20*10*10-3) 0.12+ (1/3) (20*6*10-3) 0.62

A rod has a moment of inertia of 1/3 ML2... but this gives me the wrong answer!
 
Last edited:
Lisa... said:
I have tried treating the U-shaped piece as consisting of three rods but this gives me:

Itotal= 2 I6 cm + I 10 cm =

2 (1/3) (20*6*10-3) 0.62+ (1/3) (20*10*10-3) 0.12

A rod has a moment of inertia of 1/3 ML2... but this gives me the wrong answer!
Two problems:

(1) Your teacher is assuming that the "vertical" rods are 10cm long, and the horizontal "bottom" piece is 6cm long.

(2) While the two vertical rods are being rotated about one end, the horizontal rod is not. Treat that one as just a point mass (as far as rotation is concerned).
 
Okay great! Now I understand the whole thing :) Thank you VERY much Doc Al! The trick was the second point you've mentioned, I need to remember that :)
 
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