Lecture_15

Lecture_15 - The second part just says that the sum of the...

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The second part just says that the sum of the external torques must be equal to zero. hus for rigid objects in equilibrium there are no linear accelerations or angular 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. x Axis of rotation r Let’s drill a hole in the end of the handle and hang it from a peg. his becomes the axis of rotation for the W 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! 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 ody can be considered to produce a torque due to its weight 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 . cg x Pivot (fulcrum) 9.4 Newton’s 2 nd Law for Rotational Motion ma F = Torque is the rotational analog of force. α is the rotational analog of acceleration. o what is the rotational analog of mass??? τ So what is the rotational analog of mass??? ? =
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First, let’s consider a point mass that is undergoing circular motion and accelerating: By Newton’s 2 nd Law, there is a tangential force: r a T T T ma F = And, there is a torque produced by this force: m T T rF rF = = θ τ sin T rma = ⇒τ ut But, α r a T = So, ) ( r rm = ) ( 2 mr = I = I is called the moment of Inertia . It is the rotational analog of mass. a ranslational Motion ma F I = Newton’s 2 nd Law Translational Motion Rotational Motion For a point mass: 2 mr I =
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The moment of inertia, I , not only depends on the mass, but also on how the mass is distributed relative to the axis of rotation.
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Lecture_15 - The second part just says that the sum of the...

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