# Lab #10 - 1 Introduction Objective The purpose of this lab...

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1 Introduction: Objective: The purpose of this lab was to study rotational motion and explore the inertial behavior of different shapes of masses by comparing them to each other. We measured the translational acceleration of the pulley to analyze the validity of the assumption that the pulley exhibits rotational motion consistent with that of a disk, cylinder, and both together. We also examined the differences of inertia between a disk and cylinder by adding different masses on a string attached to a pulley to produce increasing forces and so calculate angular acceleration and moment of inertia. Theory: Moment of inertia is the tendency of an object to resist a change in motion, which depends on its mass. We can say that the denser an object’s mass, the less rotational inertia the object will have. For a rigid body that rotates about a fixed axis, Newton’s Second Law of Motion states: τ = Iα, where τ is the magnitude of the total torque (force), I is the moment of inertia of the body, and α is the angular acceleration. The rotational motion of a cylinder depends on its mass and its inner and outer radius. This relationship can be expressed as . Likewise, a disk is nothing but a cylinder without inner radius. Hence, its inertia is a function of its mass and its outer radius. Mathematically, this relationship can be illustrated as . Description: We aligned the pulley tangential to the circumference of the rotary motion sensor pulley. Three different masses were hung on a cord with downward direction to generate a force on this sensor. PASCO Capstone Software, firstly used in this semester course, was set to record angular acceleration. After this, we measured the radii and masses of a disk and brass cylinder. The radius of the pulley on the rotary sensor was also measured and recorded. We found moment of inertia of the brass cylinder by using and to find the moment of inertia of the disk. We collected this data by placing the rotary