PHY 2048L Experiment #8.1-8.2: Rigid-body rotation about a moving axis and Moment of Inertia, Full lab report

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Purpose: To study rigid-body rotation about a moving axis. Theory: The moment of inertia of a rigid body can be expressed as I = c M R2 M is the mass of the object, R is the radius and c is a co... nstant 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 Method and Apparatus: Large and small solid spheres, large and small solid cylinders, large and small thin-walled hollow cylinders, large and small thin-walled hollow spheres. 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 them from rest. Repeat until tables one and two are complete. Results Comparison and Error Analysis: 8.1: Both the large and small objects of the same shape arrived at the bottom of the incline at the same time for all rigid bodies used (solid and thin-walled hollow spheres and cylinders). The solid spheres reached the bottom of the incline at a speed of 1.4m/s and the solid cylinders reached the bottom of the incline at a speed of 1.35m/s. The thinwalled hollow cylinders reached the bottom of the incline at a speed of 1.17m/s and the thin-walled hollow spheres reached the bottom of the incline at a speed of 1.28m/s. The thin-walled hollow cylinder reached the bottom faster than the solid cylinder. The solid sphere reached the bottom faster than the thin-walled hollow cylinder. [Show More]

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