Physics - Rotation Question with Solution | TestHub

The relation between linear velocity and angular velocity is given by $\vec{v}=\vec{\omega }\times \vec{r}$.

The relation between tangential linear acceleration and angular acceleration is given by $\vec{a}=\vec{\alpha }\times \vec{r}$.

The angular momentum is defined as the cross product of the position vector and linear momentum, $\vec{L}=\vec{r}\times \vec{p}$.

The torque is defined as the cross product of the position vector and force, $\vec{\tau }=\vec{r}\times \vec{f}$.

Comparing these with the given options, the correct set of equations is $\vec{v}=\vec{\omega }\times \vec{r}$, $\vec{a}=\vec{\alpha }\times \vec{r}$, $\vec{L}=\vec{r}\times \vec{p}$, $\vec{\tau }=\vec{r}\times \vec{f}$.

Answer: $\vec{v}=\vec{\omega }\times \vec{r}$, $\vec{a}=\vec{\alpha }\times \vec{r}$, $\vec{L}=\vec{r}\times \vec{p}$, $\vec{\tau }=\vec{r}\times \vec{f}$