Rotational Motion

Kinematics

I.         Description of Rotation

            A.        Variables rotate through angle

            B.        Angles measured in radians

            C.        Separate from but may impact linear motion

II.        Angular Displacement (Dq)

            A.        Axis of rotation

            B.        Rigid body

            C.        Def: angle through which body rotates

            D.        Units

                        1.         Degrees

                        2.         Revolutions

                        3.         Radians: arc length (s)/radius (r)

            E.        Clockwise in negative, counterclockwise is positive

III.       Angular Velocity (w)

            A.        Angular displacement/time

            B.        Based on angle not distance

            C.        Units: radians/second

IV.      Angular acceleration (a)

            A.        Rate at which angle changes

            B.        Unit: radians/second²

V.        Angular vs. Tangential Variables

            A.        Tangent is at right angles to radius

            B.        Tangential speed (v_T) is magnitude of velocity

            C.        Proportional to radius

            D.        Proportionality constant is angular velocity

            E.        Tangential Speed

                        1.         

            F.        Tangential Acceleration

                        1.         

VI.      Centripetal vs. Tangential Acceleration

            A.        Acceleration along radius

            B.        From circular motion use

            C.        Since    ,                       

            D.        Non-Uniform use Pythagorus and Tangent

                        1.         a² = a_c² + a_T²

                        2.         tan q = a_T/a_c

VII.     Rolling Motion

            A.        Wheel (object) rotates around axle

            B.        No slipping at point of contact

            C.        Linear motion = rotation of tire

            D.        v = linear speed = d/t = tangential speed = s/t = rw

            E.        a = tangential acceleration = a_T = ra