Physics - Rotation Question with Solution | TestHub

Use the rigid-body velocity relation:

$v_P=v_C+\omega \times r_{P/C}\Rightarrow v_C=v_P-\omega \times r_{P/C}$

From the figure: P is the topmost point of the disk, so $r_{P/C}=R\hat{j}=1\hat{j}$ m, and $\omega =2$ rad/s clockwise as drawn.

Rotational velocity of P about C: magnitude $\omega R=2\times 1=2$ m/s; at the top point of a clockwise-rotating disk it points along +X:

$\omega \times r_{P/C}=2\hat{i}$ m/s

$v_C=2\hat{j}-2\hat{i}=(-2\hat{i}+2\hat{j})$ m/s

Answer: (C) $-2\hat{i}+2\hat{j}$