PROBLEM 1. (5 points) An object is made up of two parallel (stuck to each other), concentric uniform disks of radii R₁ and R2, with R2 > R₁. Each disk has mass M. There is no relative motion between the disks. This object has a light string wrapped around its smaller disk of radius R₁. The other end of the string is firmly attached to a fixed point. The string unwraps without sliding as the object drops vertically. If the object is initially at rest, find the speed of its center of mass after it has dropped by a height h. (Assume that is given. The moment of inertia of a uniform disk of mass m and radius r around an axis passing through its center and perpendicular to its plane is Iem = mr²). PROBLEM 2. (5 points) A uniform disk of mass M and radius R rotates around a vertical frictionless axle with angular speed wo. A point particle of mass m and speed vo collides in a direction along the tangent of the spinning disk. The direction of the velocity of the particle is the same as the direction of rotation of the spinning disk. Then the particle sticks on the rim of the disk, and both objects spin together. Find the (linear) speed of the particle after it has stuck to the rim of the disk. Ignore the effects of gravity. (For a uniform disk: Icm = MR²). PROBLEM 3. (5 points) A uniform ball of mass M and radius R rolls up (without sliding) on an inclined plane which makes an angle with respect to the horizontal. If the coefficient of friction between the ball and the inclined plane is μ, find the magnitude of friction. (You are given g. The moment of inertia of a uniform ball with respect to an axis passing through its center is Icm = MR²).