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PHY183-Lecture27 - Systems of Particles and Extended...

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March 6, 2006 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Spring Semester 2006 Lecture 27 March 6, 2006 Physics for Scientists&Engineers 1 2 Systems of Particles and Systems of Particles and Extended Objects Extended Objects ! In our previous discussions this semester we have always treated the location of objects as a single point “A car is located at x = 5.5 m…” ! Of course, the car is not ALL at x =5.5 m ! The natural choice for the location of the car is the center of gravity (center of mass) of the car ! The center of gravity of an object is the point in which we can imagine all of the mass of the object to be concentrated March 6, 2006 Physics for Scientists&Engineers 1 3 The Center of Gravity ! We support an object such that the object stays balanced and does not rotate ! There are only two forces The force of gravity The force of the pin supporting the object ! Equilibrium = forces are such that Net force is zero Net torque is zero => F g is attached directly below the supporting point ! Here, the center of gravity is marked with a red dot March 6, 2006 Physics for Scientists&Engineers 1 4 Effect of the Center of Gravity ! Suppose we support the same object from the same pin, but the center of gravity is not directly below the support point ! The forces are the same The forces still sum to zero ! However, now there is a net torque because the angle ! between the gravitational force vector and the moment arm between the two forces
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