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Previous Year Question (PYQs)
1
A rigid body is rotating at the rate of $3$ radians per second about an axis $AB$, where
$A(1,-2,1)$ and $B(3,-4,2)$.
The velocity of the point $P(5,-1,-1)$ of the body is
Solution
Direction vector of axis
$\vec{AB}=(2,-2,1)$
Unit vector along axis
$\hat n=\dfrac{(2,-2,1)}{3}$
Angular velocity
$\vec\omega=3\hat n=(2,-2,1)$
Position vector of $P$ relative to $A$:
$\vec r=(4,1,-2)$
Velocity
$\vec v=\vec\omega\times\vec r=3\vec i+8\vec j+10\vec k$
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