Question

In: Physics

What is a tensor itself? What is tensor notation used for? What is differencce between a...

What is a tensor itself?
What is tensor notation used for?

What is differencce between a tensor and a vector?

Solutions

Expert Solution

1] In Physics, we generally deal with Scalars, Vectors and Tensors.

A Scalar is a physical quantity which is described by its magnitude(numeric value). For example temperature.

A Vector is a physical quantity which is described by two things namely magnitude and direction. For example Velocity, acceleration.

A Tensor is physical quantity which is described by three things namely magnitude, direction and the plane of action.(Action Plane) For Example stress is tensor which will have nine components. Assume a 3 * 3 matrix for this. A stress tensor will have magnitude, direction and which plane the component acts on.

2]A tensor of rank (m, n), also called a (m, n) tensor, is defined to be a scalar function of m one-forms and n vectors that is linear in all of its arguments. Tensors will have magnitude and two directions example stress and strain.The second order tensors are symbolized by bold letters.

3]The elements of the tensor are functions of position and the tensor forms which is known as a tensor field. The tensor is defined at every point within a region of space (or space-time), rather than just at a point, or collection of isolated points.Tensors, generally consist of multi-dimensional arrays of numbers, or functions.

A tensor may consist of a single number, where in it is referred to as a tensor of order zero which is a scalar. Tensor of order one is known as a vector.


Related Solutions

What is the advantage of using scientific notation over decimal notation? What is the difference between...
What is the advantage of using scientific notation over decimal notation? What is the difference between weight and mass?
a) prove the derivative of a tensor is a tensor b.) prove that the the direct...
a) prove the derivative of a tensor is a tensor b.) prove that the the direct product of two tensors is a tensor
Prove that the covariant derivative of an arbitrary tensor is a tensor of which the covariant...
Prove that the covariant derivative of an arbitrary tensor is a tensor of which the covariant order exceeds that of the original by one.
The notation used in the above problem is called symbolic notation. Alternatively, we can use the...
The notation used in the above problem is called symbolic notation. Alternatively, we can use the 4-digit octal notation to specify, which is defined as follows: • Digits from left (most significant) to right (least significant): [special bits][owner bits][group bits][world bits] • Special bit digit = (4 if setuid) + (2 if setgid) + (1 if sticky), 0 for none of them • All other digits = (4 if readable) + (2 if writable) + (1 if executable), 0 for...
What is the notation used in the textbook to represent dollar's exchange rate against euro? If...
What is the notation used in the textbook to represent dollar's exchange rate against euro? If dollar appreciates against euro from yesterday to today, does this mean the exchange rate gets bigger or smaller using the notation you get from #1? Why? If dollar depreciates against euro, will this make American goods more expensive or less expensive to Eurozone buyers? Why? How does fixed exchange rate differ from floating exchange rate? How does currency union differ from dollarization?
12. How is constructed the deformation tensor?
12. How is constructed the deformation tensor?
what is 0.060 meters squared in scientific notation? what is 0.0000176 meters cubed in scientific notation?...
what is 0.060 meters squared in scientific notation? what is 0.0000176 meters cubed in scientific notation? what is 0.764 centimeters in scientific notation? what is 0.00764 meters in scientific notation? what is 1.833 centimeters squared in scientific notation? what is 0.000184 meters squared in scientific notation? what is 0.0000167 meters cubed in scientific notation? what is 8.965 g/cm3 in scientific notation? what is 1.052 g/cm3 in scientific notation? what is 8982.04 kg/m3 in scientific notation? what is 1053.89 kg/m3 in...
WHAT ARE THE DIFFERENCES BETWEEN TCP/IP AND UDP IN TERMS OF OSI LAYERS AND DEFINITION ITSELF?...
WHAT ARE THE DIFFERENCES BETWEEN TCP/IP AND UDP IN TERMS OF OSI LAYERS AND DEFINITION ITSELF? PLEASE GIVE BREIFE EXPLANATIONS WITH PICTURES AND EXAMPLES WITH EASY ENOUGH TO MEMORIZE AND UNDERSTAND
Why isn't set-builder notation used for defining functions?
In set-builder notation, we use | to show givens, yet there isn't really a standard symbol to show givens when defining functions. So why don't we just import the symbol from set-builder notation so that it becomes standardised?
Why are computer addresses described with hexadecimal notation? Why isn't the binary number system used? What...
Why are computer addresses described with hexadecimal notation? Why isn't the binary number system used? What is BCD?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT