# A wheel in uniform motion about an axis passing through its centre

#1

A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational and rotational) equilibrium because, no net external torque is required to sustain its motion.
However, the particles that constitute the wheel do experience a centripetal acceleration towards the ’ centre. How do you reconcile this fact with the wheel begin in equilibrium?How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion?

#2

The centripetal acceleration in a wheel arise due to the internal elastic forces which in pairs cancel each other. So the system remains in equilibrium during rolling. [i] In a half wheel, the system is not symmetrical so, direction of angular momentum does not coincide with the direction of angular velocity and hence an external torque is required to maintain the rotation.