1) An object is in the form of a solid disk of radius 6 meters and height 3 meters. The central axis of the disk coincides with the z-axis, and the bottom is in the xy-plane with the center at the origin. The non-uniform disk is given by p (rho)= 3r where r is the horizontal distance from the z-axis: r = sqrt (x^2+y^2). If a horizontal tangential time dependent force F(t) = 4t^2 is applied to the rim of the disk at r = 6 and z = 2meters, find the angular velocity of the object after 7 seconds.
2) A thin solid disk has radius 5 meters, and non-uniform surface mass density A?A? = 4r, where r is the distance from the center of the disk. The disk is in the xy-plane with its center at the origin. A small 3kg mass is located on the positive z-axis at z= 7.
(a) Find the total mass of the disk.
(b) Find the gravitational force between the disk and the point mass.