![UD CALC (241 ONLY) W/1 TERM ACCESS >IB](https://www.bartleby.com/isbn_cover_images/9781337051545/9781337051545_largeCoverImage.gif)
(a)
To write:
An integral expression for moment of inertia
Solution:
Explanation:
1) Concept:
The moment of inertia of a particle of mass m about an axis is defined to be
2) Calculations:
The given body about which the moment of inertia needs to be found is a thin sheet in the shape of a surface
And density function is
Therefore, the mass of each element is
And we have to find the moment of inertia about
The distance of each element from the
Therefore,
Moment of inertia of each element about
The moment of inertia of total sheet about
Conclusion:
An integral expression for moment of inertia
(b)
To find:
The moment of inertia about
Solution:
Explanation:
1) Concept:
Use the formula:
Where
2) Given:
Density
3) Calculations:
The given equation of cone is
Therefore,
The vector equation of surface
Differentiating with respect to
Then,
Therefore,
From concept,
The moment of inertia about
But
Therefore, above integral becomes,
Since,
Using polar coordinates,
The above integral becomes,
By integrating with respect to
By applying the limits of integration,
By simplifying,
Integrating with respect to
By applying the limits of integration,
Thus,
Conclusion:
The moment of inertia about
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Chapter 16 Solutions
UD CALC (241 ONLY) W/1 TERM ACCESS >IB
- the correct answer is C could you please explainarrow_forwardWhich of the functions shown below is differentiable at z = 2? Select the correct answer below: о -7-6-5-4-3-2- −7 −6 −5 −4 −3-2 1 2 4 5 6 -7-6-5-4-3-2- -7-6-5-4-3 2 45arrow_forwardQuestion Given the graph of f(z) below, find the graph of the derivative of f(z). Select the correct answer below: ° ° 129 -7-6-5-4-3-2 -7-6-5-4-3-2-1123456 ° ° °arrow_forward
- Question Find the open interval(s) of f(x), graph given below, where f'(x) is negative. -3-2-1 1 2 4 5 6 Give your answer in interval notation. For example, (2, 4) U (6,∞). Provide your answer below:arrow_forwardthe correct answer is Ccould you please show me how to do it using the residue theoremarrow_forwardUse the information to find and compare Δy and dy. (Round your answers to four decimal places.) y = x4 + 7 x = −3 Δx = dx = 0.01 Δy = dy =arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285741550/9781285741550_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134438986/9780134438986_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780134763644/9780134763644_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781319050740/9781319050740_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9780135189405/9780135189405_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337552516/9781337552516_smallCoverImage.gif)