# Lab 8.docx - Experiment 8.1 Theory The moment of inertia of...

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Experiment 8.1:Theory: The moment of inertia of a rigid body can be expressed as I = c M R2, where M is the mass of the object; R is the radius and c is a constant that is determined from the shape of the object. c= 2/5 for a solid sphere, c= ½ for solid cylinders and disks, c= 2/3 for thin walled hollow spheres and c=1 for thin walled hollow cylinders. If the rigid body rolls down a surface without slipping, the mechanical energy of the rigid body is conserved and only the conservative force of gravity does work on the rigid body. The speed of the center of mass of the rigid body at the bottom of the incline can be found using the equation: v = √(2gh)/(1+c) This speed does not depend on the mass or radius of the object. All objects of the same shape will have the same speed at the bottom of an incline because they have the same c value, and the smaller c is, the greater an object’s speed will be.Experimental Apparatus: Large and small solid spheres, large and small solid cylinders, large and small thin-walled hollow cylinders, large and small thin-walledhollow spheres. Experimental Method: 1.Measure and record the height of the inclined plane. 2.Race two round rigid bodies from the top of the inclined plane by releasing themfrom rest. Repeat until tables one and two are complete.