Does a rigid object in uniform rotation about a fixed axis satisfy the first and second conditions for equilibrium?

Explanation:

a rigid object in uniform rotation about a fixed axis does not satisfy both the condition of equilibrium .

First condition of equilibrium is that net force on the body should be zero.

or F net = 0

A body under uniform rotation is experiencing a centripetal force all the time so F net ≠ 0

So first condition of equilibrium is not satisfied.

Second condition is that , net torque acting on the body  must be zero.

In case of a rigid object in uniform rotation , centripetal force is applied towards the centre ie  towards the  line joining the body under rotation with the axis .

F is along r

torque = r x F

= r F sinθ

θ = 0 degree

torque = 0

Hence 2nd condition is fulfilled.

a. spokes of a wheel.

as indicated in the question radial contains rad, also found in radius, so the fracture's would span the radius.