Question

A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translation plus rotational) eqilibrium because no net external force ot torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripletal acceleration directed towards the centre. How do you reconcile this fact with the wheel being 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 ?

Answer 1

A wheel is a rigid body. The centripetal accelerations of the particle of the wheel arise due to the internal elastic forces which cancel out in paries.
In a half wheel, the distribution of mass about its centre of mass (through which axis of rotation passes) is not symmertical. Therefore, the direction of angular momentum of the wheel does not coincide with the direction of its angular velocity. Hence, an external torque is required to maintain the motion of the half wheel.