-101040a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k,ii.B = 1+ 2) - k, C = 31 - 1 + 2k .b. The angular velocity of a rotating rigid body about an axis of rotation is given by ai = 4i +j -2k. Find the linear velocity of a point P on the body whose position vector relative to a point onthe axis of rotation is 2i-3j+k.ii. Find the moment of inertia tensor from the given picture.300 mmP.T.O.iv.Given point P = (1, -2, 3) and vector A = yz i+x1- yx k , express this vector in cylindricalcoordinate system.V.a. Show that the contraction of the outer product of the tensors AP and B, is an invariant.b. Show that every tensor can be expressed as the sum of two tensors, one of which issymmetric and the other skew-symmetric in a pair of covariant or contra variant indices.vi. The 4-oz top with radius of gyration about its spin axis of 0.62 in. is spinning at the rate p =3600 rev/min in the sense shown, with its spin axis making an angle e = 20° with the vertical.The distance from its tip O to its mass center G is r = 2.5 in. Determine the precession 2 of thetop and explain why O gradually decreases as long as the spin rate remains large. An enlargedview of the contact of the tip is shown.Enlargod viowof tip contactvii.Find the S.F. and B.M. of the beam given below and draw it.50 KN10 KNm140 kN2m +le4m- 4 mA hollow steel shaft transmits 200 kW of power at 150 rpm. The total angle of twist in a lengthof 5 m of the shaft is 5". Find the inner and outer diameter of the shaft if the permissible shareviii.stress is 60 GPa and rigidity modulus is 80 GPa.Two identical blocks A and B are connected by a rod and rest against vertical and horizontalplanes, respectively, as shown in fig. If sliding impends when O = 45°, determine the coefficientof friction u, assuming it to be the same at both floor and wall.

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a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k, B= 1 + 21- k, Č = 31 - 1 + 2k . ii. b. The angular velocity of a rotating rigid body about an axis of rotation is given by = 4i +j - 2k. Find the linear velocity of a point P on the body whose position vector relative to a point on the axis of rotation is 21-3j+k.

a. Find the volume of the parallelepiped whose edges are represented by A = 2i - 3j + 4k, B= 1 + 21- k, Č = 31 - 1 + 2k . ii. b. The angular velocity of a rotating rigid body about an axis of rotation is given by = 4i +j - 2k. Find the linear velocity of a point P on the body whose position vector relative to a point on the axis of rotation is 21-3j+k.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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