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valentinak56 [21]
2 years ago
12

The moment of inertia about the axis of a solid cylinder is _____ the moment of inertia of a cylindrical shell having the same m

ass and radius.
SAT
1 answer:
marin [14]2 years ago
6 0

The moment of inertia about the axis of a solid cylinder is <u>less than</u> the moment of inertia of a cylindrical shell having the same mass and radius.

<h3>How to calculate moment of inertia?</h3>

Mathematically, the moment of inertia for a solid cylinder is calculated by using this formula:

I = (1/2)mr²

<u>Where:</u>

  • m is the mass.
  • r is the radius.

In conclusion, the moment of inertia about the axis of a solid cylinder would be <u>less than</u> the moment of inertia of a cylindrical shell that has the same mass and radius because the mass of the solid cylinder must be taken near the axis of rotation, which makes it smaller.

Read more on moment of inertia here: brainly.com/question/3406242

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No product results in -1, hence δlmn is NOT a right triangle showing that  lydia's assertion is incorrect

<h3>Perpendicular lines</h3>

In order to determine whether triangle lmn  is right-angled, we need to determine the slope of lm, ln, and mn first as shown:

For the slope of lm:

m_{lm} = \frac{2-0}{2-0}\\ m_{lm} =2/2\\m_{lm} =1

For the slope of ln:

m_{ln} = \frac{-1-0}{2-0}\\m_{ln} =-1/2\\

For the slope of mn:

m_{mn} = \frac{-1-2}{2-2}\\m_{ln} =-3/0 = \infty\\

  • If any of the two lines is perpendicular, hence the triangle lmn is right-angled.

  • To check, we will take the product of the slopes and see if it is equivalent to -1.

Product of slope lm and ln

m_{lm}\times m_{ln} = 1 \times -1/2\\m_{lm}\times m_{ln} = -1/2

Since no product results in -1, hence δlmn is NOT a right triangle showing that  Lydia's assertion is incorrect

Learn more on slopes here: brainly.com/question/3493733

8 0
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