Question

$\mathbf{}\mathit{T}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{}\mathit{m}\mathbf{(}\mathit{\omega }\mathbf{\times }\mathit{r}\mathbf{)}\mathbf{\cdot }\mathbf{(}\mathit{\omega }\mathbf{\times }\mathit{r}\mathbf{)}$

Short answer

B is an axial vector.

Step-by-step solution

Given information.

Physics definitions are given.

Definition of Kinetic Energy.

Define Kinetic Energy.

$\mathbf{}\mathit{T}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{}\mathit{m}\mathbf{(}\mathit{\omega }\mathbf{\times }\mathit{r}\mathbf{)}\mathbf{\cdot }\mathbf{(}\mathit{\omega }\mathbf{\times }\mathit{r}\mathbf{)}$

Write about the nature of various vectors.

It is proved earlier that the vector product of an axial and a polar vector results in a polar vector.

It is also known that the scalar product of polar vectors is a scalar vector.

Make an appropriate conclusion.

The above reasoning implies that$T=\frac{1}{2}m(\omega \times r)\cdot (\omega \times r)$ is a scalar.