IGNOU PHE 4 2018 - For a particle undergoing circular motion with an angular velocity w i

Question

For a particle undergoing circular motion with an angular velocity w in a circle of
radius r show that:

ω x (ω x r) = – ω²r

25 Jan 2018

Answer :

Word Count : 327

We will numerically verify the vector identity: \[ \mathbf{\omega} \times (\mathbf{\omega} \times \mathbf{r}) = -\omega^2 \mathbf{r} \] for a particle undergoing circular motion. ### Step 1: Define Given Quantities - Let the angular velocity vector be \( \mathbf{\omega} = (0, 0, \omega) \), assuming rotation about the \( z \)-axis. - Let the position vector of the particle be \( \mathbf{r} = (r_x, r_y, 0) \), since it moves

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