Q. 20

# 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?

As the system is the symmetrical system, the centripetal acceleration in a wheel arise due to internal elastic which exists in pair and cancel each other.

In the second part of question, in half wheel the distribution of mass about centre of mass is not symmetrical.

Therefore, the direction of angular momentum doesn’t coincide with the direction of angular velocity and hence an external torque is required to maintain rotation.

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