• Given appropriate information, set up the necessary integrals (in an appropriate choice of coordinate system) to calculate the following: ■ Total mass of a 2D lamina ■ All three second moments of a 2D lamina ■ The radius of gyration about the x- and y-axes of a 2D lamina
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- |%oY li. 019. iss 019 • Vector A has magnitude 2 and vector B'has magnitude 3. The angle Ø between Ẩ and B is known to be 0°, 90°, or 180°. For each of the following situations, state what the value of Ø must be. (In each situation there may be more than one correct answer. (a) Ẩ .B`=0, (b) Ẩ ×B° =0, (c) A .B =6, (d) Ẩ .B =-6, (e) (Magnitude of Ẩ ×B° =6) between 4md s magnitude 2 and vector / . The angle a betweenfa 0", 90", or 180. the folowing situations, st O must be. On each situat e than one correct answer 30 betweenA"a the angle betwe -4i +2 -1 of 6) دعاء صاحب حسین 4:19, äc luI 21.02.04 IIQUESTION 1 Give a physical interpretation of what is meant by the curl of a vector. Suppose a vector function A is given by A=-yi + xj and another vector function B is given by B = xj. 1.1 1.2 1.3 Calculate (i) the curl of A: (ii) the curl of B: V x A and Vx B. In which direction are the curls pointing? Hence what can you say about their divergence and why?SOLVE FOR THE RESUL TANT OF A = 2.5 N, 16° NORTH OF EMST AND B-ION , 40° EAST OF NORTH USING LAW OF SINE AND COSINE. YOU CAN VERIFY YOuR ANSWER USING THE COMPONENT METHOD.
- For this question, can you explain how we get the integral from dFz to Fz. Can you also explain how im supposed to know which proportion to use? In some similar question we use proportions such as dQ/dl and in other question we use dz/d theta. How do i know which proportion to use for the question?Replace the polar equation r= 8 cos 0 + 4 sin 0 with an equivalent Cartesian equation. Then identify the graph. The equivalent Cartesian equation is (Type an equation using x and y as the variables.)| Apps G Gmail YouTube Maps UST Cloud Campus Desmos | Graphing... 0.034 QUESTION 3 Problem A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire. L. r image Solution a) Let us first derive the expression for the tension. By Newton's First Law Save All Answers Click Save and Submit to save and submit. Click Save All Answers to save all answers. 29°C L ight rain
- Problem 4: For vectors B =- î - 4ĵ and A = - 3î - 2ĵ.b) In your own words describe first moment of area for any shape and its importance. With reference to the shape below about the axis s - s, describe the position of the centroid. 40 mm 10 mm A 10 mm 60 mm 10 mm 30 mm0.034 QUESTION 3 Problem A solid uniform ball with mass m and diameter d is supported against a vertical frictionless wall by a thin massless wire of length L. a) Find the tension in the wire. d. r Solution a) Save All Ans Click Save and Submit to save and submit. Click Save All Answers to save all answers. 29°C Ligh 31 OType here to search
- Two vectors are defined below. A = -3ỹ - 92 • Find P, if P = ẢxB. Also, draw Vector P. Finally, how would you find the direction of Vector P with your right hand? B = -6x + 5ŷ . If the norm of Vector A equals 9.49, what would the angle between Vector A and Unit Vector Y be when placed tail-to-tail?The density of a spherical solid at a point P = (x, y, z) is given by f(x, y, z) = c(x² + y² + z²) , c it is a positive constant. When attempting a displacement from the point P = (1,2,3) of the interior of this solid, according to the vector below: a = (1, 1/2, -1) The density trend is: A) decrease B) increase to the maximum C) keep constant D) decrease to the maximum E) increaseQuestion 5 A solid E is made up of a cylinder, with radius 3 units and height 4 units, and a hemisphere attached on top of the cylinder, as shown in the figure below. Figure 05 (a) The projection of solid E onto the yz-plane can be described as follows: Projection of E onto yz-plane = {Cy, z) | – 3 sy< 3,0 < z 5 4 + /9– yz} (i) Describe the projection of solid E onto the xy- and xz-plane. (ii) Describe solid E. (b) (i) Consider the integration over the solid domain E x dv. Rewrite this integration as an iterated integral with dz first, followed by dy, then dx. (ii) Rewrite the iterated integral in Question 5(b)(i) by converting to cylindrical coordinates. (iii) Hence, compute the integral.