Question

Velocity vector and acceleration vector in a uniform circular motion are related as.

Answer 1

They are related as $\bold{\underline {v}\,.\,\underline a }= \bold{0}$

• In a uniform circular motion, the magnitude of the speed does not change during the travel and only the instantaneous direction changes.
• This speed is always directed along the tangent to the circle at a given point. (refer to the figure attached)
• For any circular motion, the must-have acceleration is the centripetal acceleration that is directed towards the centre of the circular locus (if the motion has a tangential acceleration, it has a tangential acceleration additionally).
• Therefore, both the directions of the tangential speed and the centripetal acceleration are orthogonal to each other (perpendicular: one is 90 degrees apart from the other).
• In mathematics, 2 vectors ($\underline p$ , $\underline q$) that are perpendicular to each other have a quality that their dot product ($\underline p\,.\, \underline q$) equal to zero vector ($\bold 0$) which is written as $\undeline p\,.\, \underline q = \bold 0$.
• This quality can be considered when dealing with the velocity vector and the acceleration vector in a manner $\underline v\,.\, \underline a =\bold 0$.

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