An end of a light wire rod is bent into a hoop of radius r. the straight part of the rod has length l; a ball of mass m is attached to the other end of the rod. the pendulum thus formed is hung by the hoop onto a revolving shaft. the coefficient of friction between the shaft and the hoop is µ. find the equilibrium angle between the rod and the vertical.

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination.at the turning point, how far is the second student from the destination?