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  • A wheel in uniform motion about an axis passing through its center and perpendicular to its plane is considered to be in mechanical equilibrium because no net external force or torque is required to sustain its motion.

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

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The wheel is a rigid elastic body. When a wheel is in uniform motion about the axis passing through its centre and perpendicular to the plane of the wheel, every particle of the wheel is also in a circular motion about the above axis. The centripetal acceleration acting on each particle is directed towards the axis of rotation due to elastic forces which are in pairs.

To set a half wheel into uniform motion about an axis passing through the centre of mass of wheel and perpendicular to its plane an external torque is required. This is because in case of a half-wheel, the distribution of mass of half wheel is not symmetric about the axis of the wheel and thus the direction of angular momentum does not coincide with angular velocity.

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