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# ch09 - Chapter 9 Rotational Dynamics 9.1 The Action of...

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Chapter 9 Rotational Dynamics

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9.1 The Action of Forces and Torques on Rigid Objects In pure translational motion, all points on an object travel on parallel paths. The most general motion is a combination of translation and rotation.
9.1 The Action of Forces and Torques on Rigid Objects According to Newton’s second law, a net force causes an object to have an acceleration. What causes an object to have an angular acceleration ? TORQUE

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9.1 The Action of Forces and Torques on Rigid Objects The amount of torque depends on where and in what direction the force is applied, as well as the location of the axis of rotation.
9.1 The Action of Forces and Torques on Rigid Objects DEFINITION OF TORQUE Magnitude of Torque = (Magnitude of the force) x (Lever arm) F = τ Direction: The torque is positive when the force tends to produce a counterclockwise rotation about the axis. SI Unit of Torque: newton x meter (N·m)

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9.1 The Action of Forces and Torques on Rigid Objects Example 2 The Achilles Tendon The tendon exerts a force of magnitude 790 N. Determine the torque (magnitude and direction) of this force about the ankle joint.
9.1 The Action of Forces and Torques on Rigid Objects 790 N F = τ m 10 6 . 3 55 cos 2 - × = ( 29 ( 29 m N 15 55 cos m 10 6 . 3 N 720 2 = × = - τ

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9.2 Rigid Objects in Equilibrium If a rigid body is in equilibrium, neither its linear motion nor its rotational motion changes. 0 = x F = 0 y F = 0 τ 0 = = y x a a 0 = α
9.2 Rigid Objects in Equilibrium EQUILIBRIUM OF A RIGID BODY A rigid body is in equilibrium if it has zero translational acceleration and zero angular acceleration. In equilibrium, the sum of the externally applied forces is zero, and the sum of the externally applied torques is zero. = 0 τ = 0 y F 0 = x F

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9.2 Rigid Objects in Equilibrium Reasoning Strategy 1. Select the object to which the equations for equilibrium are to be applied. 2. Draw a free-body diagram that shows all of the external forces acting on the object. 1. Choose a convenient set of x , y axes and resolve all forces into components that lie along these axes. 1. Apply the equations that specify the balance of forces at equilibrium. (Set the net force in the x and y directions equal to zero.) 1. Select a convenient axis of rotation. Set the sum of the torques about this axis equal to zero.
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ch09 - Chapter 9 Rotational Dynamics 9.1 The Action of...

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