A wheel in uniform motion about an axis passing through its centr… - Vidyadip

Question

A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) 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 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?

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Answer

Wheel is a rigid rigid elastic body. It is in uniform motion about axis passing through it’s centre and perpendicular to the plane of wheel. Each particles of wheel which constitute the wheel are in circular motion about above axis and each particle will experience a centripetal acceleration directed towards axis of rotation due to elastic forces which are in pairs.
In a half wheel the distribution of mass of mass of half wheel is not symmetric about the axis of wheel. Therefore the direction of angular momentum and angular velocity does not coincide. Hence the external torque is required to maintain the motion in half wheel.

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