Ch 09 Rotational Dynamics

Ch 09 Rotational Dynamics - Chapter 9 Rotational Dynamics...

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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 (Curvilinear or linear), all points on an object travel on parallel paths.
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The most general motion is a combination of translation and rotation
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(Translational + Rotational) Motion Translational Motion
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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 .
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9.1 The Action of Forces and Torques on Rigid Objects Definition of Torque Magnitude of Torque = (Magnitude of the force) x (Lever arm) l F = τ ± Direction: The torque is positive when the force tends to produce a counterclockwise rotation about the axis, and negative when the force tends to produce a clockwise rotation. ± SI Unit of Torque : newton.meter (N·m) ± Torque ( τ ) is defined as the force applied multiplied by the moment arm (lever arm).
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Why do acrobats carry long bars?
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Sign Convention ± A counterclockwise torque is designated as positive ( + ) ± A clockwise torque is designated as negative ( )
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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. 790 N l F = τ m 10 6 . 3 55 cos 2 × = l o () ( ) m N 15 55 cos m 10 6 . 3 N 720 2 = × = o
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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 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
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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. 3. Choose a convenient set of x , y axes and resolve all forces into components that lie along these axes. 4. Apply the equations that specify the balance of forces at equilibrium. (Set the net force in the x and y directions equal to zero.) 5. Select a convenient axis of rotation. Set the sum of the torques about this axis equal to zero. 6. Solve the equations for the desired unknown quantities. The choice of the axis of rotation is completely arbitrary , because if an object is in equilibrium, it is in equilibrium with respect to any axis whatsoever .
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External Forces: Gravitational Normal Frictional Tension… Sum of external forces Σ F x = ma x Σ F y = ma y Sum of external torques Σ F = Στ = I α Equilibrium a x = 0 a y = 0 α = 0 Nonequilibrium a x 0 a y 0 α≠ 0 Rigid Objects in Equilibrium
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9.2 Rigid Objects in Equilibrium
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This note was uploaded on 12/03/2010 for the course PHY phy135 taught by Professor Weighgabriel during the Fall '10 term at University of Toronto.

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Ch 09 Rotational Dynamics - Chapter 9 Rotational Dynamics...

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