EXPERIMENT9BRotational Motion 2 Moment of inertia Objectives •to familiarize yourself with the concept of moment of inertia, I, which plays the same role in the description of the rotation of a rigid body as mass plays in the description of linear motion •to investigate how changing the moment of inertia of a body affects its rotational motion APPARATUSSee Figure 3a. THEORYIf we apply a single unbalanced force, F, to an object, the object will undergo a linear acceleration, a, which is determined by the unbalanced force acting on the object and the mass of the object. The mass is a measure of an object's inertia, or its resistance to being accelerated. Newton’s Second Law expresses this relationship: F = maIf we consider rotational motion, we find that a single unbalanced torque τ = (Force)(lever arm)#produces an angularacceleration, α, which depends not only on the mass of the object but on how that mass is distributed. The equation which is analogous to F = ma for an object that is rotationally accelerating is τ = I α. (1) where the Greek letter tau (τ) represents the torque in Newton-meters, αis the angular acceleration in radians/sec2and Iis the moment of inertiain kg*m2. The moment of inertia is a measure of the way the mass is distributed on the object and determines its resistance to angular acceleration. #In this lab the lever arm will be the radius at which the force is applied (the radius of the axle). This is due to the fact that the forces will be applied tangentially, i.e., perpendicular to the radius. The general form of this relationship is θτsin**armleverforce=, where θis the angle between the force and the lever arm. However, in this experiment θis 90° and sin(90°) = 1.
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Every rigid object has a definite moment of inertia about any particular axis of rotation. Here are a couple of examples of the expression for I for two special objects: One point mass m on a weightless rod of radius r (I = mr2): xyzOFigure 1Two point masses on a weightless rod (I = m1r12+ m2r22): yxz0Figure 2