Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying on its circumference, as shown in the figure. The smaller disks are initially in contact with each other, with an angular separation between their centers. They are made to roll without slipping in opposite directions, with constant angular velocities and 2 while the large disk is held stationary. The time at which the smaller di

Step-by-step solution

Let the radius of the large disk be R and the radius of the small disks be r . We are given r = R/50 , which implies R = 50r . The centers of the small disks move along a circular path of radius R + r = 50r + r = 51r . When the two small disks are in contact, the distance between their centers is 2r . The angular separation between their centers is given by the arc length (which is approximately the chord length for small angles): (R + r) = 2r (51r) = 2r = 2 51 rad The small disks roll without slipping on the stati