well, friction must equal centripetal force. As radius increases, centripetal force gets bigger, and friction cannot hold it. So your problem bothers me as it is written as if the moving inward makes the block more unstable, which is not true.
So where is the block unstable?
mu*mg=m*w^2 r
.5*9.8=2.2^2 *r
r=1.01 meter from the center. Inside that radius, it will stay, outside, it will fly off.
A platform rotates at an angular speed of 2.2 rad/s. A block rests on the platform a distance of 0.3m from the axis. Static friction coeffient= 0.5. Without any external torque acting on the system, the block is moved towards the axis. Ignore the moment of interia of the platform. Determine the smallest distance in cm from the axis the block can be moved and still remain in place as the platform rotates.
I know that the answer is between 17 and 23cm.
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