Question:
The correct vector relation between linear velocity $ \vec{v} $ and angular velocity $ \vec{\omega } $ in rigid body dynamics is ( where $ \vec{r} $ is the position vector)
The correct vector relation between linear velocity $ \vec{v} $ and angular velocity $ \vec{\omega } $ in rigid body dynamics is ( where $ \vec{r} $ is the position vector)
Updated On: Jun 3, 2024
- $ \vec{\omega }=\vec{v}\times \vec{r} $
- $ \vec{v}=\vec{r}/\vec{\omega } $
- $ \vec{v}=\vec{\omega }\times \vec{r} $
- $ \vec{r}=\vec{v}\times \vec{\omega } $
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The Correct Option is C
Solution and Explanation
The vector relation between linear velocity $ \vec{v} $ and angular velocity $ \vec{\omega } $ in rigid body dynamics is
$ \vec{v}=\vec{\omega }\times \vec{r} $ .
$ \vec{v}=\vec{\omega }\times \vec{r} $ .
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.