Rotary Movement Responses to Applied Torques

Have previously discussed linear kinematics

Now presenting rotational kinematics

        Angular displacement
               the change in the angle

        Angular Velocity
               change in angle over time (omega  = theta / t)

        Linear displacement
               change in position along the arc (d = radius * theta)

        Linear velocity
               speed of motion along the arc (v = radius * omega)

        **  Show Overhead #1  **

        Angular acceleration
               change in angular velocity over time (a = þw / t)

Relationship between Torque, Rotational Inertia, and Angular Acceleration

        Previously showed F = ma

               Show old overheads ,   F = ma

        Present that angular acceleration = torque / rotational inertia

               a = T / I

               What the heck is rotational inertia

               Remember F = ma (a large mass hinders change in movement)
                       explain again

               Now consider T = Ia
                       same property (a large inertia resists change in rotation)

               Rotational Inertia = mass * radius of gyration (K) squared
                       (for our purposes, consider K to be center of mass)

               **  Show Radius of Gyration Overhead  **

               Explain how requires larger torque to begin to move / slow down (a)

               Present new overheads between Torque, acceleration, Rotational Inertia