## How do you find velocity from cylindrical coordinates?

Position, Velocity, Acceleration where vr=˙r,vθ=rω, v r = r ˙ , v θ = r ω , and vz=˙z v z = z ˙ . The −rω2^r − r ω 2 r ^ term is the centripetal acceleration. Since ω=vθ/r ω = v θ / r , the term can also be written as −(v2θ/r)^r − ( v θ 2 / r ) r ^ .

**Where do we prefer spherical coordinate system?**

Spherical coordinates are preferred over Cartesian and cylindrical coordinates when the geometry of the problem exhibits spherical symmetry. For example, in the Cartesian coordinate system, the surface of a sphere concentric with the origin requires all three coordinates (x, y, and z) to describe.

**Is strain rate tensor symmetric?**

The strain rate tensor and the rotation rate tensors are the symmetric and antisymmetric parts of the velocity gradient tensor, respectively.

### How do you find velocity in spherical coordinates?

- Vx, Vy, and Vz be the x,y, and z components of the velocity V in Cartesian co-ordinates i.e.
- V= iVx + jVy + kVz.
- Then the r, th, ph components of V in spherical coordinates are given by.
- Vr = |V| = sqrt(Vx^2+Vy^2+Vz^2) . . . . . (
- Vth = Vz . . . . . . . . . ( 2) and.
- Vph = V cos(ph_v) = Vcos[atan2(Vx,Vy)] . . . . . (

**What is the strain tensor 47 for spatial displacement gradient?**

Strain Tensors 47 which deﬁnes the spatial displacement gradient tensor as follows. Spatial displacement gradient tensor ⎧ ⎪⎨ ⎪⎩ j(x ,t def = u(x

**What is the material time derivative of the strain tensor?**

1 101 Strain Tensor E The material time derivative of the material strain tensor has already been derived for the physical interpretation of the deformation rate tensor: A more direct procedure yields the same result: E F dF T d dt 1 ( ) 2 E FF T 1

#### What does the longitudinal strain measure?

1 1 0 0 0 0 ee e e ee e ⋅⋅= ⋅ ⋅= tet 53 Similarly, the stretching of the material in the y -direction and the z – direction: The longitudinal strains contain information on the stretch and unit elongation of the segments oriented in the x y and z -directions (in the deformed or actual configuration).

**What is linearized stretch in terms of the strain tensors?**

Stretch in terms of the strain tensors: But in Infinitesimal Strain Theory, T ≈ t. So the linearized stretch and unit elongation through a direction given by the unit vector T ≈ t are: 1 1 2 λ= t − ⋅⋅ t et T 1 2 TET x λ= + ⋅⋅ 0 1 1 2 01 x xx d xx dx λ λ λ 0 1 1 12 01 x x x d xx dx λ λ λ