Lab4Rotations

Lab4Rotations - 1 of 1 Physics 2010 Laboratory 4:...

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1 of 1 1 Physics 2010 Laboratory 4: Rotational Dynamics NAME ___________________________ Section Day (circle): M Tu W Th F Section Time: 8a 10a 12p 2p 4p TA Name: ________________________ This lab will cover the concepts of moment of inertia and rotational kinetic energy. These concepts play the same roles in rotational motion as mass and kinetic energy do for straight-line motion. Instructions: Make safety a priority. This experiment uses fairly heavy rolling objects. There is a risk of toe injury as well as damage to equipment. Background Information 1. Moment of Inertia The moment of inertia , I , (also called moment and rotational inertia ) of a body is a measure of how much a body resists changing its rate of rotation about some axis. Similar to mass in linear motion, the larger a body’s moment, I, the more work it takes to increase the body’s rotation rate. The moment of inertia is always defined with reference to a particular axis of rotation often a symmetry axis, but it can be any axis, even one that is outside the body. The moment of inertia of a body about a particular axis is defined as: (1) The moment of inertia of a point mass m orbiting at radius r about an axis, is I = mr 2 (2) If many point masses make up the body, equation 1 can be rewritten as I = I 1 + I 2 + … + I i = m 1 r 1 2 + m 2 r 2 2 + … + m i r i 2 (3) where r i is the distance of mass m i from the axis of rotation. If the body is a continuous object of some arbitrary shape, then performing the sum requires techniques of calculus. In this course, we tell you the answer for various shapes. For a disk of mass M and radius R (see Fig. 1), the moment of inertia through the center of symmetry is I disc = ½ MR 2 . (4) Notice that the thickness of the disk doesn't enter into the expression for I disc , so the expression for I is the same for a solid cylinder as it is for a flat disk. A cylinder is just a very thick disk. Figure 1. Solid disk with axis of symmetry, uniform mass and density.
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2 of 2 2 The expression in equation I disc = ½ MR 2 is only true for a uniform disk or cylinder. If the object is a hoop or a thin-walled cylinder, a different formula is used. The moment of inertia of a hoop or thin- walled cylinder is I hoop = MR 2 . Because all the mass is at the same radius from the axis, making it more resistant to changes in its rate of rotation. In this experiment you will determine I for a wheel made of a
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Lab4Rotations - 1 of 1 Physics 2010 Laboratory 4:...

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