I am given the velocity $v$ of the point $C$ of the base of the cone which **rolls without slipping** on a horizontal plane. Now the question asks me to find the angular velocity of the cone.

Attempt:

I found the angular velocity of the cone about its own axis using the condition for pure rolling:

$v= R\omega_{OC} \implies \omega_{OC}= \dfrac v R$

Now, the answer is incomplete because we have to include the angular velocity due to rotation about the point O. I am facing difficulty in this part. How do I go about solving it further? The distance OC is $R\cot\alpha$

Edit:

I analysed it further and here are my workings:

Let $\omega$ be angular velocity about O

$\omega = \dfrac{d\theta}{dt}= \dfrac{ds}{R\cot \alpha dt}= \dfrac{v}{R\cot \alpha}$

Is my approach correct?