Uncategorized: Practice Problem & Solution
If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau}$ be the torque of this force about the origin, then: (2009)
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
Torque is defined as the cross product of position vector and force: $\vec{\tau} = \vec{r} \times \vec{F}$.
By the properties of cross products, the resulting vector $\vec{\tau}$ is perpendicular to both $\vec{r}$ and $\vec{F}$.
Therefore, their dot products must be zero: $\vec{r}\cdot\vec{\tau} = 0$ and $\vec{F}\cdot\vec{\tau} = 0$.
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