1. The moment of inertia is a property of an object that resists a change in angular acceleration. It plays the same role for rotation as mass plays for linear motion. For example, if we have two objects of mass ml and m2 (m1 >~ m2) experiencing a common force F then by Newton's second law the acceleration of each object is a1 = Ffml and a2 = JED/mg. Since the rst mass is larger than the second then the rst object accelerates more slowly. The equivalent Newtonis law in rotation is T = I or where I is the moment of inertia: a: the angular acceleration, and T the torque. By analogy to linear motion, if two objects experiences a common torque then the object with the higher moment of inertia will have a slower angular acceleration. The moment of inertia for a set of objects of mass ma- rotating about a common axis is dened as 2 I = E rat-r}E i where n is the distance of the ith object to the axis of rotation. If there are many particles that make 11p a larger object then this sum transforms into an integral, I = [f/prgdl', V where p is the mass density and V the volume of the object. In this exercise we will explore moment of inertia by rolling two objects down an incline plane in the Experimental Math Lab Space. Consider a cylindrical shell of constant density p1 inner radius r1, outer radius R, and height H. Assume that the cylinder is oriented along the zaxis. {a} Find the mass, m... of the cylinder. (b) Show that the zaxis goes through the centre of mass of the cylinder (c) Assume that the cylinder rotates around the zaxis. Find the moment of inertia of the cylinder in terms of the mass m. \"Thy does the height of the cylinder not matter? (d) Compute the moment of inertia from {1c} for the specic cases of a solid cylinder {r1 = U) and a thin cylindrical shell (r1 > R). If the objects race down an inclined plane, which one reaches the bottom rst