PAP111_Lecture12 - PAP111 Lecture12 AngularPosition,...

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PAP 111  Mechanics and Relativity  Lecture 12 Rotation Motion of a Rigid Object about a Fixed Axis Angular Position, Velocity and Acceleration Rotational Kinematics Rotational Kinetic Energy Moments of Inertia Torque and Angular Acceleration
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Consider you are in a moving train and run  from the back of the train towards the  front. While you run the train 1. accelerates. 2. decelerates. 3. doesn’t change its  velocity.
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Then you stop… The train is now  1. faster. 2. slower. 3. at the same  velocity as you  started.
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Rigid Object In the treatment on rotation of an extended object, the  motion cannot be analyzed by regarding the object as a  particle because at any given time different parts of the  object have different linear velocities and linear  accelerations. Hence, the motion of each part of the object  has to be analyzed separately. However, the analysis is greatly simplified if we were to  assume that the rotating object is rigid. A rigid object is  one that is nondeformable – that is, the relative locations  of all particles of which the object is composed remain  constant. Note: All real objects are to some extent deformable. The rigid object is an useful approximation for  situations when the deformation is negligible.
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Blue Ray Disc as a Rigid Object Through the rotation of the blue ray disc with the axis of rotation at  the center of the disc, we will try to gain an understanding on  physical quantities such as angular position, angular displacement,  angular velocity and angular acceleration. First, let us identify an arbitrary  particle at point P in the disc. This  particle is located at a distance  r    from the origin O of the disc. 1
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Rotation of Blue Ray Disc As the Blue Ray disc rotates counterclockwise about its axis of  rotation, the position of P changes as it maintains a distance r from  the origin while the line OP sweeps through an angle  θ Hence, for a rigid object rotating  about a fixed axis, it is convenient to  represent its points by the co- ordinate (  r , θ   ), where  r  is the distant  of the point to the fixed axis, while  θ   is the angle measured counter- clockwise from some fixed reference  line. 1
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Specification of a Rigid Body by  θ Because the disc is a rigid object, as the particle moves along  a circle away from the fixed reference line, every other particle  on the object rotates through the same angle  θ . Thus, we can  associate the angle  θ  with the entire rigid object as well as  with an individual particle. This means that the concept of an 
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