When angular velocity has a given value in the problem and I want to take the vector cross product of it with vector position; Does it have $\hat k$ component or not?
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1 Answer
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Consider a rod AB hinged at end A rotating with angular speed $w$ in the clockwise sense as seen from top.
Now, direction of $w$ is $-\hat k$ (considering right handed system). For all intents and purposes that is, if you want to take the cross product, you must use $-\hat k$ with the value given in the problem.
