The vector field D* = e*r (cos2q) r3 is defined within the spherical shell whose inner and outer radii are determined as r = 1 ve r = 2, respectively. Calculate $D* · ds

Q: Find the curl of the vector field F =

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Q: A=(2x2-3y)ax+(2x-y2)ay   Prove the Stokes theorem for the triangular linear path in the shape that…

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Q: Determine the divergence of these vector fields: 1 T cos 8 a, + r sin 0 cos o a, + cos 0 a

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Q: 2.2 Express the following points in cylindrical and spherical coordinates: (a) P(1, –4, –3) (b) Q(3,…

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Q: A = (3, 5, -7) B = (2, 7, 1). Find A + B. A- B, A, B, A B, and the cosine of the angle between A

A: A→=3i^+5j^-7k^B→=2i^+7j^+1k^ A→+B→=3i^+5j^-7k^+2i^+7j^+1k^=5i^+12j^-6k^

Q: as gh ed 8. A cone with base radius R and height h is located on horizontal table. A horizontal…

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Q: Let F be the vector field F(r, y, z) = 2²i – sin yj + (2.rz + 622)k. Compute divergence and gradient…

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Q: Given the vector field, G =y Find the following: i. G at Q ii. Scalar component of G at Q in the…

A: To determine: (1) The vector field G at Q for the given vector field   Given vector, G=yax-2xay+4az…

Q: Q(2) Consider the two vectors A= 31 - B =-i-4j, Calculate the angle between vectors A) 146" B) 47,7…

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Q: Ex.1/ Resolve the 100" force along OA and OB. Sol/ 1. 40 100N 100 30 Sin 40 sin(180-30-40)

A: Given values:- OC→=100 N ----(1) We have to resolve this force to find the value of P & Q…

Q: if a=6 and b=12 determine the angle θ between the two cables

A: given that,a=6b=12FAB=12 lb

Q: Calculate the areas of the following surfaces using the differential surface area dS p=2,0 ≤z≤ 5,…

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Q: Evaluate both sides of the Divergence Theorem of the given vector field D = ye" ax + z(xy)? ay + (x…

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Q: A (-3; 2; 0), B (0; 0; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC = 201 and FBD = 192,…

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Q: The normal force is always perpendicular to the surface. True False

A: As per Newton's third law, for every action force, there is a reaction force.

Q: Ql: Show that: sin 8 cos o A, A sin ở sin o -cos 0 cos o cos 8 sin o -sin e cos o cos 0|| A, - sin o…

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Q: lands at the point having the coordinates (1.84, 1.18) m, determine tne polar coordinates or the…

A: x= 1.84m    and y= 1.18m

Q: Evaluate both sides of the Divergence Theorem of the given vector field D = ye* ax + z(xy)? ay + (x…

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Q: Demonstrate the sides of the triangle in terms of vector. Please refer to the given.    Given:…

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Q: 1 A) L= zmit – mgRcos0 What are the Lagrange equations for the particle in the given figure B)…

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Q: Given the function y =3xyz2î + 2xy³j-x2yzk Find the curl Vxu a. 3yz'i + 6xy2j - x²yk b. Зyz? + 6ху?-…

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Q: Evaluate the commutator L,, L, L,- (a) h'L, (b) 0 (c) h'L, (d) h°L.

A: In rotational mechanics, Angular momentum holds a similar place as linear momentum. If Net torque on…

Q: The vector field G is described by the vector function shown below. Evaluate G at point P(-3, 4, 5)…

A: We have a given vector field G and we need to evaluate G at point P.  So, we need to put x = -3 ,…

Q: Compute and sketch the vector assigned to the points P (0, 6, –1) and Q = (4, 1,0) by the vector…

A: Given, P =(0, 6, -1)Q = (4, 1, 0)Vector field, F = xy, z2, x

Q: Show that the points with position vectors 3i-5j, 4į+j, 6¿+13j are collinear. If the point whose…

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Q: Consider a vector field of A = (2x-z) i + xyj - x ²k taken over the region (a cube) bounded be x =…

A: Vectors are physical quantities that have both magnitude and direction. Scalars on the other hand…

Q: A (-3; 2; 0), B (0; D; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC= 201 and FBD 192,…

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Q: Express the uniform vector field F = 5ax in (a) cylindrical components; (b) spherical components.

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Q: vector field T (x.y.z) = (z/x)ax + (y/z² )ay d(T) Determine the magnitude of at P(2,7,5) dz

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Q: solve the 260 N force of fig as shown into  two components with one acting along AB  and the other…

A: Assume that the component of the force acting along AB be fB and force passing through point C be…

Q: Given a vector field A = 5x ^ 2(sin (pi*x)/2) i, find V.A at x = 1

A: Vector A = 5x².(sin (pi.x)/2)i

Q: Can you show me an example of polar coordinates? (I am an engineering student, I would like to see…

A: To give an example of polar coordinate.

Q: The field B = -2ax + 3ay + 4az mT is present in free space. Find the vector force exerted on a…

A: Given, Current, i = 2 A Magnetic field vector, B = −2ax+ 3ay+ 4az mT = B = (−2ax+ 3ay+ 4az)10-3 T…

Q: calculate F = V X (-y éxt xěy), which is the form of V × b, where bx = -y, by = x, bz = 0. We have…

A: Let F denotes the curl of the given function, Fx, Fy, and Fz denote the components of the curl.…

Q: Find the flux of the vector field F = k through the upper half of the sphere r? + y² + z2 = 4. 4pi…

A: Sphere : x2 + y2 +z2 =4 Radius = 40.5            = 2 units

Q: A spherical.cavity is made inside a sphere of density, d. If its centre lies at a distance l, from…

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Q: . Show that the vector field F(x, y) = ( 2xy, x² + 2y) is conservative. Then, find the potential…

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Q: Can two vectors, of unequal magnitude, add up to give the zerovector? Can three unequal vectors?…

A: If two vectors have equal magnitude but different directions then only their sum will be zero.

Q: .Calculate the area of the parallelogram whose two adjacent sides are formed by the vectors. A = 3i…

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Q: Vo Horizontal Field As compared to the horizontal component of the velocity at point Y, the…

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Q: 1900 N 900 N 20 30 F25 70°

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Q: 4. Find the gradient of the following scalar fields: (a) U = 4xz + 3yz (b) W = 2 p (z + 1) cos

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Q: Q6/ A vector field is given by F = sin y i + x(1+ cosy)j, evaluate a line integral over a circular…

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Q: 2. Let R = 5 xT and 0 + 90° where 0 is the angle between S and T when they are drawn with their…

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Q: Application of Stokes Theorem 3. Evaluate both sides of Stokes' theorem for the field H=6xyax -…

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Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).