Consider an arbitrarily shaped object undergoing a rotational motion in the xy plane (see figure below). Let O be a point in the xy plane along the axis of rotation, and P, N, and M are fixed points on the object located at distances r, 0.5 r, and 0.25 r, respectively. Due to the rotational motion of the object, points P, N, and M will move along their circular path. If the linear velocity of point P is vp = 4.5 m/s and it is located at distance r = OP = 1.2 m from the axis of rotation, determine the magnitude of angular velocity of points P, N, and M, and the magnitude of the linear velocity of points N and M.

Consider an arbitrarily shaped object undergoing a rotational motion in the xy plane (see figure below). Let O be a point in the xy plane along the axis of rotation, and P, N, and M are fixed points on the object located at distances r, 0.5 r, and 0.25 r, respectively. Due to the rotational motion of the object, points P, N, and M will move along their circular path. If the linear velocity of point P is vp = 4.5 m/s and it is located at distance r = OP = 1.2 m from the axis of rotation, determine the magnitude of angular velocity of points P, N, and M, and the magnitude of the linear velocity of points N and M.