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# Lab_08 - Laboratory 8 Rotational Motion II The Rotating Bar...

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Laboratory 8 Rotational Motion II: The Rotating Bar Introduction In Laboratory 6, we investigated moment of inertia and the ways in which it differs from mass. We also looked at a situation (the inclined plane) in which both translational and rotational kinetic energy come into play, and saw how rotational kinetic energy plays a role in two-dimensional inelastic collisions between extended objects. In this laboratory, we will expand our knowledge of rotational dynamics to include the concept of torque , and we will examine energy conservation in another context: a rotating bar. We will also use the rotating bar to explore the conservation of angular momentum in two situations, one of which will lead directly into our analysis of gyroscopic motion in the following laboratory. Theoretical Background: Force vs. Torque Simply put, force is something that can change the velocity of a body. Similarly, torque is some- thing that can change the angular velocity of a body. Even though forces are required to generate torques, it is important to remember that torque is not a force. Torques and forces are both vectors, so we have to deal with them using the tools of vector algebra. The magnitude of a torque experienced by a rigid object about a particular axis of rotation can be calculated using τ = r F sin ( θ ) , (1) where τ is the magnitude of the torque, F is the magnitude of the applied force, and r is the magnitude of the vector r (also known as the lever arm ) that points from the axis of rotation to the point at which the force is applied. (For diagrams, see Figures 1 and 2.) In this equation, we also have an angle θ , which is the angle subtended from r to F . What does this equation tell us? First, it tells us that we can only calculate torque relative to a particular axis of rotation - the torques an object experiences will differ depending on which axis we choose, because the r in Equation 1 will change. Second, it tells us that a force is needed to create a torque, but that not all forces create torques - a force can only create a torque if it is applied at some nonzero distance from the axis of rotation. A similar force applied further from the axis of rotation will generate more torque. An illustration of this idea is shown in Figure 1. Problem 8.1 Why is it easier to open a door by pushing on the handle than by pushing near the hinge? 65

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F F F r r r = 0 90 90 Most Torque Less Torque No Torque Figure 1: Forces applied at different distances from a pivot. Equation 1 also tells us that a force applied perpendicular to r will generate more torque than the same force applied parallel to r . Hint: What is sin ( 0 ) ? See Figure 2. F r 90 Most Torque Less Torque No Torque F r 45 F r Figure 2: Forces applied at different angles. Problem 8.2 Give a physical/geometric interpretation of F sin ( θ ) . What does this term represent?
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Lab_08 - Laboratory 8 Rotational Motion II The Rotating Bar...

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