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Unformatted text preview: Chapter 12 Chapter 12 Rotational Motion Rotational Motion q is the angular displacement angular displacement where s = r q. f 2 i 2 2 f − i Torque depends on the choice of the origin rF sin r F Torque: the Angular Analog of Force Torque: the Angular Analog of Force Torque can be thought of as an “angular force” which causes a change in angular motion. It is defined as: In (b) F sin q is the component of the force perpendicular to the door. In (c) rsin q is the component of the moment arm perpendicular to the force, defined as the lever arm. The choice is often determined by the particular application or problem. It should be noted that: In the next chapter we will define torque as a vector via the vector product: Internal Torques Cancel Internal Torques Cancel Consider an arbitrary object rotating about an axis (the bold point in the figure). Two mass elements exert equal and opposite forces on each other. The torques about the axis are: Since F 12 = F 21 and r 1 sin q 1 = r 2 sin q 2 the internal torques cancel! 12 F 12 r 1 sin 1 and 21 F 21 r 2 sin 2 Internal torques cancel in pairs just as the internal forces do. The net torque is the sum of external torques! Note that r is the distance to the axis of rotation, and I is not not equal to M r 2 cm . xample: Moment of Inertia of Two Point Masses xample: Moment of Inertia of Two Point Masses A dumbbell shaped object of two equal masses a distance l apart is subjected to a torque, t , about an axis ¼ of the way between the two masses. How long will it take for the system to rotate through an...
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This note was uploaded on 04/16/2008 for the course PHYS PHYS2A taught by Professor Hicks during the Spring '08 term at UCSD.
 Spring '08
 Hicks
 Force

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