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Unformatted text preview: Lecture 19 Torque and Angular Momentum Principle 1 Review from Last Time Rotational Kinematics Angular velocity: magnitude and direction Angular acceleration: magnitude and direction 2 Torque What causes angular acceleration? What causes an object to start spinning or to spin up? Recall that acceleration is caused by application of a force. What about change in angular velocity? DEMO/Experiment: Bike wheel (hang different mass weights, also at different distances) more weight means larger ~ . But, ALSO, depends on distance from rotation axis. And ALSO, depends on direction that the force is applied: 90 between force and radius vector gives largest angular acceleration. So, we see that angular acceleration is caused be an applied force (similar to linear acceleration), but the amount of angular acceleration also depends on the lever arm. So ~ is proportional to | r || F | sin (DRAW) This looks like the cross product again! Torque ~ = ~ r ~ F Torque is somewhat analogous to force. It gives rise to angular acceleration. But, notice it has different units than force. You can think of it as the amount of twist associated with an applied force. PUZZLERS: Torque DEMO - which way does disk tip (Gimball) 3 More on the Moment of Inertia So, the angular acceleration is proportional to torque. What is the proportionality con- stant? It is the moment of inertia that we defined last lecture....
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