A sphere rotates about a diameter.

When a sphere rotates about a diameter, the diameter acts as the axis of rotation.

The particles on the axis of rotation have a perpendicular distance $r = 0$ from the axis. Therefore, their linear speed $v = r\omega = 0$ and centripetal acceleration $a_c = r\omega^2 = 0$. Thus, they experience no linear acceleration.

Particles on the surface have varying perpendicular distances from the axis, so their linear speeds $v = r\omega$ vary depending on their position. They also experience centripetal acceleration, meaning they have non-zero linear acceleration.

All particles of a rigid body rotating about a fixed axis possess the same angular speed $\omega$.