(a) Show that the polar radius of gyration kO of the area shown is approximately equal to the mean radius Rm (R1 R2) 2 for small values of the thickness t R2 R1 (b) Determine the percentage error introduced by using Rm in place of kO for the following values of t Rm 1, 1 4, 1 16 ...

a From Problem 925 And Then Now Then And For Or k 12 Jo 3 R R 3 A dA R 7rdr 7 R R 3r ...

(a) Show that the polar radius of gyration kO of the area shown is approximately equal to...

Question:

(a) Show that the polar radius of gyration kO of the area shown is approximately equal to the mean radius Rm = (R1 + R2)/2 for small values of the thickness t = R2 ˆ’ R1.

(b) Determine the percentage error introduced by using Rm in place of kO for the following values of t/Rm: 1, 1/4, 1/16.

(a) Show that the polar radius of gyration kO of the area shown

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Vector Mechanics for Engineers Statics and Dynamics

ISBN: 978-0073212227

8th Edition

Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell

See More Books

Question Posted: Sep 17, 2010 12:17 AM

See More Questions

Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point P.
Determine the polar moment of inertia and the polar radius of gyration of the shaded area shown with respect to point O. R=a cos 20
Determine the polar radius of gyration of the shaded area about point 0. 0.43a
When we create our own Market Limitations In the mid-1960s a new electronics company was founded with a unique high-tech product a new type of computer. Thanks to its engineering know-how LOCKDOWN...
Sherbrooke Toboggan Company manufactures toboggans for the Canadian market. The product goes through three manufacturing processes: forming, sealing, and assembly. In the forming department, the wood...
Gill Bates is the CEO of a large company. His compensation is based on current profitability. He is considering undertaking one of two investments available to the company: (a) one that yields...
The lab-on-a-chip product in Figure 25.13 incorporates the inventions in the innovation map of Figure 25.10. Carry out a patent search to determine whether all of the technological inventions in...
Shown below in T-account format are the changes affecting the retained earnings of Brenner-Jude Corporation during 2011. At January 1, 2011, the corporation had outstanding 105 million common shares,...
EEE Co manufactures three products, A, B and C, details of which are as follows: Product A Selling price ($ per unit) 288 Direct materials (kg per unit) 22 Contribution margin ($ per unit) 76 Product...
A voltmeter of resistance 500 and a milliammeter of 1.0 resistance are used to measure a resistance by ammeter voltmeter method. If the voltmeter reads 20 V and the milliammeter 100 mA, calculate...
(a) Determine by direct integration the polar moment of inertia of the area shown with respect to point O. (b) Using the result of part a, determine the moments of inertia of the given area with...
Determine the polar moment of inertia and the radius of gyration of the isosceles triangle shown with respect to point O.
Find the mass of the solid bounded by the planes x + z = 1, x - z = -1, y = 0, and the surface y = z. The density of the solid is (x, y, z) = 2y + 5.
In Problems 9-16, find the indicated matrices, if possible. \[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array} ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2 \\-1...
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of $80 \%$ micoden and $20 \%$ water, Ingredient II is made up of $30 \%$ micoden, $50 \%$ bixon, and \(20...
In Problems 9-16, find the indicated matrices, if possible. \[[\mathrm{A}]=\left[\begin{array}{rr}1 & 2 \\4 & 0 \\-1 & 3 \\2 & 1 \end{array} ight] \quad[\mathrm{B}]=\left[\begin{array}{rr}4 & 2 \\-1...
In Problems 4-13, decide whether the statement is true or false. If it is false, tell what is wrong. In the notation $* \operatorname{Row}+(3,[A], 4,5)$, the target row is 3 .
The information is based on the spreadsheet as shown Suppose Ingredient I is made up of $80 \%$ micoden and $20 \%$ water, Ingredient II is made up of $30 \%$ micoden, $50 \%$ bixon, and \(20...
You have a controlling interest if: a. you own more than 20% of a companys ordinary shares. b. you are the president of the company. c. you use the equity method. d. you own more than 50% of a...
Use translations to graph f. f(x) = x-/2 +1
A seawater sample has a density of 1.03 g/mL and 2.8% NaCl by mass. A saturated solution of NaCl in water is 5.45 M NaCl. How many liters of water would have to be evaporated from 1.00 x 10 6 L of...
Following are the hybrid parameters for a network
If the Y parameters for a network are known to be
Find the Z parameters in terms of the ABCD parameters
With regard to the production possibilities frontier (PPF), an efficient point is a point that is: ?
Within the context of rapidly evolving regulatory landscapes and heightened ethical scrutiny, how do advanced organizations navigate the ethical complexities of technological innovation and...
Write a program that accepts an integer limit and an integer value and that prints a complete line of output reporting the multiples of value uptil the limit . Keep prompting the user for a value...

(a) Show that the polar radius of gyration kO of the area shown is approximately equal to...

Question:

Step by Step Answer:

a From Problem 925 And Then Now Then And For Or k 12 Jo 3 R R 3 A dA R 7rdr 7 R R 3r ...View the full answer

Vector Mechanics for Engineers Statics and Dynamics

Students also viewed these Mechanical Engineering questions