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lecture19 - 9.2 Rigid Bodies in Equilibrium A rigid body is...

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9.2 Rigid Bodies in Equilibrium A rigid body is a fixed collection of masses (i.e. it’s not a point particle). Examples of rigid bodies: Every object is, in principle, a rigid body. In general, a rigid body could be moving linearly (translational motion) and it could also be spinning (rotational motion). Thus, for a rigid body to be in dynamic equilibrium, it must not be accelerating translationally or rotationally. Therefore, the following must be true: 0 = x F 0 = y F 0 = ext τ Translational Equilibrium Rotational Equilibrium
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The second part just says that the sum of the external torques must be equal to zero. Thus, for rigid objects in equilibrium there are no linear accelerations, or angular accelerations. 9.3 Center of Gravity The weight of a rigid body can cause a torque on an object without any other external forces acting on the object. Take a hammer, for example. Let’s drill a hole in the end of the handle nd hang it from a peg. x Axis of rotation r and hang it from a peg. This becomes the axis of rotation for the hammer. If I release the hammer, it will swing or rotate about this axis. There must be a torque on the hammer causing this rotation. Where does it come from? It’s due to the weight of the hammer ! But where does the force act??? It acts at the CM of the hammer! W Now you can see that there is a positive torque on the hammer due to its weight, causing the hammer to rotate ccw. rW rF = = θ τ sin
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Define Center of Gravity (cg): The Center of Gravity of a rigid body is the point at which the weight of the body can be considered to produce a torque due to its weight. If gravity is the only external force acting on a rigid body, then the rigid body will be in dynamic equilibrium if the axis of rotation is placed at the center of gravity of the body . x
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This note was uploaded on 08/04/2009 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.

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lecture19 - 9.2 Rigid Bodies in Equilibrium A rigid body is...

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