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2053Lecture11 - Rotational Dynamics Topics of Discussion...

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Unformatted text preview: Rotational Dynamics Topics of Discussion Rotating Bodies & Center of Mass Moment of Inertia Definition of Torque Rigid Bodies In Equilibrium Newton's Second Law for Rotational Motion Center of Gravity Given a system of N bodies each of mass mi located at the point (xi, yi) in the xy-plane, the center of gravity is given by xcm = N i= N mi xi mi N i= ycm = i= N mi yi mi i= Moment of Inertia For a system of N particles each of mass mi located a distance ri from an axis of rotation, the moment of inertia I is defined to be I= N i= mi ri . The SI unit of the moment of inertia is kgm2.The moment of inertia depends on the location and orientation of the axis relative to the location of the masses that comprise a system of particles. Definition of Torque Let F be the magnitude of an applied force that is perpendicular to a lever arm of length l. Then the torque produced by the force F is given by = Fl where the SI unit of torque is the Nm. If the force produces a counterclockwise motion then the torque is positive. If the force produces a clockwise motion then the torque is negative. Remarks The lever arm is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. The magnitude of the torque depends on the location of the axis of rotation. Forces that act through the lever arm produce no torque. Rigid Bodies in Equilibrium In component form, the sum of all forces and torques acting on a body must vanish, that is, for bodies in equilibrium Fx = 0 and Fy = 0, and =0. Newton's Second Law for Rotational Motion Let m be the mass of a body rotating a distance r about an axis of rotation with an angular acceleration . Then the sum of the torques is proportional the angular acceleration , that is = I where I = mr2 is called the moment of inertia whose SI unit is kgm2. ...
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