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A wheel is 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 its 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 elastic body which is in uniform motion about axis passing through its centre and perpendicular to the plane of wheel. The particles that constitute the wheel do experiment centripetal acceleration directed towards the centre. This centripetal acceleration arises due to internal elastic forces which cancel out in pairs. In a half wheel the distribution of mass about its centre of mass (axis of rotation) is not symmetrical. Therefore, the direction of angular momentum does not coincide with the direction of angular velocity and hence an external torque is required to maintain rotation. |
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