A platform rotates at an angular speed of 2.2 rad/s. A block rests on this platform a distance of 0.3m from the axis. (friction coefficient .5) Without any external torgue acting on the system, the block is moved toward the axis. Ignore the moment of inertia of the platform. Determine the smallest distance (in cm) from the axis the block can be relocated and still remain in place as the platform rotates

Question

A platform rotates at an angular speed of 2.2 rad/s.  A block rests on this platform a distance of 0.3m from the axis. (friction coefficient .5)  Without any external torgue acting on the system, the block is moved toward the axis.  Ignore the moment of inertia of the platform.  Determine the smallest distance (in cm) from the axis the block can be relocated and still remain in place as the platform rotates

drwls · Answer

The moment of inertia of the platform with block will decrease as the block is pushed toward the center. This will cause the angular velocity of the platform to increase. When calculating the moment of inertia and angular velocity of block distance R, ignore the I of the platform (because they tell you to. (It seems an unrealistic assumption to me). The centripetal acceleration of the block will increase as it moves to the center. At some radial distance form the axis, a static friction coefficient of 0.5 will be necessary to keep the block from slipping. That will be the answer.