PAP111_Lecture12 - PAP 111 Mechanics and Relativity Lecture...

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Unformatted text preview: 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 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. doesnt change its velocity. Then you stop The train is now 1. faster. 2. slower. 3. at the same velocity as you started. 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. 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 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 . Hence, for a rigid object rotating about a fixed axis, it is convenient to represent its points by the co- ordinate ( r , ), where r is the distant of the point to the fixed axis, while is the angle measured counter- clockwise from some fixed reference line. 1 Specification of a Rigid Body by 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 . Thus, we can associate the angle with the entire rigid object as well as with an individual particle. This means that the concept of an angular position, as defined by...
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PAP111_Lecture12 - PAP 111 Mechanics and Relativity Lecture...

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