Question
Which of the following is incorrect?(a) $\vec{v}=\vec{\omega} \times \vec{r}$(b) $\vec{a}=\vec{v} \times \vec{r}$(c) $a=\frac{d \omega}{d t}$(d) None of these
Step 1
Option (a) $\vec{v}=\vec{\omega} \times \vec{r}$ is the formula for the velocity of a particle in circular motion, where $\vec{\omega}$ is the angular velocity and $\vec{r}$ is the radius vector. This is a correct statement. Show more…
Show all steps
Your feedback will help us improve your experience
Narayan Hari and 60 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Which of the following is the correct relation between linear relocity $\bar{v}$ and angular velocity $\vec{\omega}$ of a particle? (a) $\overline{\boldsymbol{v}}=\overline{\bar{F}} \times \bar{\omega}$ (b) $\vec{v}=\overrightarrow{(\dot{a}} \times \overline{\boldsymbol{r}}$ (c) $\overrightarrow{\mathbf{u}}=\bar{r} \times \vec{v}$ (d) $\overrightarrow{\mathbf{g}}=\overline{\bar{v}} \times \vec{r}$
Which of the following are always true, and which are not always true? Give reasons for your answers. \begin{array} { l } { \text { a. } \mathbf { u } \cdot \mathbf { v } = \mathbf { v } \cdot \mathbf { u } } \\ { \text { b. } \mathbf { u } \times \mathbf { v } = - ( \mathbf { v } \times \mathbf { u } ) } \\ { \text { c. } \quad ( - \mathbf { u } ) \times \mathbf { v } = - ( \mathbf { u } \times \mathbf { v } ) } \\ { \text { d. } ( c \mathbf { u } ) \cdot \mathbf { v } = \mathbf { u } \cdot ( c \mathbf { v } ) = c ( \mathbf { u } \cdot \mathbf { v } ) \quad \text { (any number } c ) } \\ { \text { e. } c ( \mathbf { u } \times \mathbf { v } ) = ( c \mathbf { u } ) \times \mathbf { v } = \mathbf { u } \times ( c \mathbf { v } ) \quad \text { (any number } c ) } \\ { \text { g. } \quad \mathbf { u } \cdot \mathbf { u } = \mathbf { u } = 0 } \\ { \text { h. } ( \mathbf { u } \times \mathbf { v } ) \cdot \mathbf { u } = \mathbf { v } \cdot ( \mathbf { u } \times \mathbf { v } ) } \end{array}
Vectors and the Geometry of Space
The Cross Product
Which of them is not correct? a) j x j = 0 b) j x k = i c) j x i = k d) j x i = -k
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD