Intro to Rigid Body Kinematics: Fixed-Axis Rotation | Cross Products in the Casio fx-115es plus

LECTURE 08

Here the concept of rigid body kinematics is introduced. The constant nature of the relative position vector within a body experiencing pure translation is shown, and it is asserted that kinematic analysis of bodies experiencing pure translation is identical to the analysis of particles undertaken previously in the course. General plane motion is then described as a combination of pure translation and pure rotation. Pure rotation (i.e. fixed-axis rotation) is then highlighted and equations relating angular velocities and accelerations to linear velocities and accelerations are presented. It is pointed out that the calculus-based relationships between angular displacement, velocity, and acceleration mirror their translational counterparts. The vector method of relating angular velocities and accelerations to instantaneous linear velocities and accelerations is also introduced. An example problem is presented wherein a rectangular prism is mounted to two ball joints defining a relatively simple-to-visualize axis of rotation. Angular velocity and acceleration are given for the body, and instantaneous linear velocity and acceleration are found for vertices of the rectangular prism. Assuming the acceleration value given is constant and the angular velocity value is an initial value, the angular velocity and displacement are found after a given elapsed time of motion. The angular displacement is used to determine the total distance traveled by one of the vertices of the prism. Lastly, the location of one of the ball joints is changed and the vector method is used to determine the instantaneous linear velocity and acceleration of one of the vertices of the prism. The Casio fx-115es plus is used to perform the necessary cross-products to find these vectors.

Playlist for MEEN203 (Dynamics):
   • MEMT 203: Dynamics  

This lecture was recorded on June 26, 2018. All retainable rights are claimed by Michael Swanbom.

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