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Rotational Motion

# Rotational Motion - PHY 122 LAB Rotational Motion...

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PHY122 Labs ( © P. Bennett, JCHS) -1- 10/25/06 PHY 122 LAB : Rotational Motion Introduction: In this lab we will see how a constant torque creates a constant angular acceleration for a rigid body rotating about its CM. We’ll see that the moment of inertia depends on the rotation axis for a given object. Finally, we’ll look at rotational motion from an energy viewpoint. Applications of the moment of inertia concept include the design of crankshafts, rotary rides at a fair, or the baton twirling of a marching band leader. Text Reference: Young & Freedman 9.1-5. Theory A stone dropped into a well falls a distance Z = 0.5 g t 2 . If we convert this equation to the angular domain, it says Θ = 1/2 α t 2 . We study similar behavior in this lab. In more detail, a rigid object free to rotate about a principle axis with moment of inertia I will accelerate according to τ = r*F = I* α , eq. 1 where τ is the applied torque (given by the vector cross product of r and F), and α is the angular acceleration in rad/sec 2 . Recall π radian = 180 degrees. Take care that τ , α and I are in consistent units. “ I ” is readily calculated for symmetric objects, and has the form I = β MR 2 , where β is a dimensionless fraction (0-1) that depends on the shape of the object and the rotation axis. A 3-dimensional object has 3 principal values of I, corresponding to 3 independent possible axes of rotation. These values would all be the same for a sphere through its center, but would all be different for a low symmetry object. Thus, for example, a rectangular

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Rotational Motion - PHY 122 LAB Rotational Motion...

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