[Physics] Rolling of a disk and sphere

Question

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has more angular velocity. the moment of inertia of a sphere is less than the disk so it that if the moment of inertia is less then the angular velocity is more?
Also the Mass and shape specifications of both objects is same.

Also if a sphere's angular velocity is more then why aren't tyres of cars,etc spherical?

Answer 1

I am confused regarding the fact that when a disk is rolling on an inclined plane without slipping and similarly a solid sphere is rolling on an inclined plane without slipping then the sphere has more angular velocity. the moment of inertia of a sphere is less than the disk so it that if the moment of inertia is less then the angular velocity is more?

Assuming that they have the same mass and same dimensions (except that the disk is hollow), then yes, the sphere has more angular velocity because it has a lower moment of inertia.

Also if a sphere's angular velocity is more then why aren't tyres of cars,etc spherical?

Other than the fact that spherical tyres are quite impossible to implement, look bad, and probably unsafe, you'll probably want the higher moment of inertia, as it will make your ride smoother due to its higher resistance to change in motion. This is the reason why your engine has a flywheel - without it your ride will be jerky and unsmooth.