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A rigid body is spinning about a fixe...

A rigid body is spinning about a fixed point (3,-2,-1) with an angular velocity of 4 rad/s, the axis of rotation being in the direction of (1,2,-2). Find the velocity of the particle at point (4,1,1).

Text Solution

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`vecomega=4 ((hati+2hatj-2hatk)/(sqrt(1+4+4)))=4/3(hati+2hatj-2hatk)`
`vecr= vec(OP) -vec(OA)`
`=(4hati+hatj+hatk)-(3hati-2hatj-hatk)`
`= hati+3hatj+2hatk`
`vecv=vecomegaxxvecr=4/3(hati+2hatj-2hatk)xx(hati+3hatj+2hatk)`
`= 4/3 ( 10 hati-4hatj+hatk)`
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