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chapter08

# chapter08 - Chapter 8 Rotational Equilibrium and Rotational...

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Chapter 8 Rotational Equilibrium and Rotational Dynamics

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Force vs. Torque Forces cause accelerations Torques cause angular accelerations Force and torque are related
Torque The door is free to rotate about an axis through O There are three factors that determine the effectiveness of the force in opening the door: The magnitude of the force The position of the application of the force The angle at which the force is applied

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Torque, cont Torque, , is the tendency of a force to rotate an object about some axis = r F is the torque Symbol is the Greek tau F is the force r is the length of the position vector SI unit is N . m
Direction of Torque Torque is a vector quantity The direction is perpendicular to the plane determined by the position vector and the force If the turning tendency of the force is counterclockwise, the torque will be positive If the turning tendency is clockwise, the torque will be negative

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Multiple Torques When two or more torques are acting on an object, the torques are added As vectors If the net torque is zero, the object’s rate of rotation doesn’t change
General Definition of Torque The applied force is not always perpendicular to the position vector The component of the force perpendicular to the object will cause it to rotate

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General Definition of Torque, cont When the force is parallel to the position vector, no rotation occurs When the force is at some angle, the perpendicular component causes the rotation
General Definition of Torque, final Taking the angle into account leads to a more general definition of torque: r F sin F is the force r is the position vector is the angle between the force and the position vector

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Lever Arm The lever arm , d, is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force d = r sin This also gives = rF sin
Right Hand Rule Point the fingers in the direction of the position vector Curl the fingers toward the force vector The thumb points in the direction of the torque

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Net Torque The net torque is the sum of all the torques produced by all the forces Remember to account for the direction of the tendency for rotation Counterclockwise torques are positive Clockwise torques are negative
Torque and Equilibrium First Condition of Equilibrium The net external force must be zero This is a necessary, but not sufficient, condition to ensure that an object is in complete mechanical equilibrium This is a statement of translational equilibrium 0 0 0 x y or and F F F

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Torque and Equilibrium, cont To ensure mechanical equilibrium, you need to ensure rotational equilibrium as well as translational The Second Condition of Equilibrium states The net external torque must be zero 0
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chapter08 - Chapter 8 Rotational Equilibrium and Rotational...

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