# What is the relationship between torque and angular momentum for a non-point mass?

For a point mass, $$\tau=I\alpha$$ and $$L=I \omega$$.

What if we apply a force to the edge of an ellipse, if the torque is $$rF\sin\theta$$, where $$r$$ is the distance between the point where the force is applied to the centre of mass of the ellipse, then the equation relating angular momentum and this force will then be $$rFt\sin\theta=I\omega$$ or $$mvr\sin\theta=I\omega$$, where "I" will be the moment of inertia of ellipse about its centre of mass. However, $$mvr\sin\theta$$ is the angular momentum of a point mass instead of an ellipse.

What is the mistake? Thank you.