A sphere rolls on a horizontal surface. Is there any point of the sphere which has a vertical velocity?

If the ice at the poles melts and flows towards the equator, how will it affect the duration of day-night?

A hollow sphere, a solid sphere, a disc and a ring all having same mass and radius are rolled down on an inclined plane. If no slipping takes place, which one will

take the smallest time to cover a given length?

Let a unit vector along the axis of rotation of a purely rotating body and be a unit vector along the velocity of a particle P of the body away from the axis. The value of is

A body is uniformly rotating about an axis fixed in an inertial frame of reference. Let be a unit vector along the axis of rotation and be the unit vector along the resultant force on a particle P of the body away from the axis. The value of is