A Wheel in uniform motion about an axis passing through its centre and perpendicular to its plan,e is considered to be in mechanical equilibrium, because no net external force of torque is required to sustain its motion. However the particles that constitute the wheel do experience a centripetal force. The acceleration is 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 the plane? Will you require external forces to sustain the motion?

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Solution

Wheel is a rigid body , the particles that consiture the wheel do experience a centripetal acceleration directed towards the centre , this acceleration arises due to internal eleastic forces , which cancel out in pairs. In a half wheel the distribution of mass about its centre of mass (through which axis of rotation passes ) is not symmetrical , 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.

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