Question

Particle is moving on circular path with uniform speed determine ratio of angular velocity of particle w.r.t. centre and w.r.t point on circumference of circle diameter opposite.

Answer 1

Let the angular velocity of the particle about centre $c$ be ${\omega }_c$, and at point A on the circumference of circle be ${\omega }_a$

we know that angular velocity about centre of circle is $2$ times that of about angular velocity about any point on the circumference.
i.e. ${\omega }_c=2{\omega }_a$

$\frac{{\omega }_a}{{\omega }_c}=\frac{1}{2}$