A small piece of cheese is at the center of a disk of radiusRrotating about its axis. A hungry mouse is sitting at the edgeofthe disk. It will be able to eat the cheese when it is a distancer= R/4 from the center of the disk. The surface of thedisk,however, is slippery ... In the following, assume that the disk is spinning freely aboutitsaxis and that there is no net external torque acting onthesystem. a) Write expressions for the moment of inertia of the system(diskplus mouse) when the mouse is at the edge (distanceR) andwhen the mouse is at the distance r fromthe center. Themoment of inertia of the disk is I=(1/2)MR2. b) As the mouse approaches the center, does the disk speed up,slowdown, or maintain its angular velocity? c) Assuming the angular velocity is wwhen the mouse is at the edgeof the disk, find an expression forthe angular velocitywr whenthe mouse is a distance r = R/4from thecenter. d) Evaluate the angular velocity wr for the case thatthe mass of thedisk is M = 18 g, the mass of the mouse ism = 16g, and w = 4 s-1. Answer:wr =10 s-1. e) Determine if a static friction coefficient of ms =0.7 is sufficient to prevent themouse from slipping at r =R//4 for R =0.4 m. Please use g = 10m/s2.
