AP Physics - Rotational Kinematics

θ ω

Introduction

  • Objects can have several types of motion

    • Figure skater

      • Gliding on skates

        • Translational

        • Straight line motion

      • Spinning on skates

        • Rotational

        • Spinning about a fixed axis

    • Wheels, gears, hands on clock, rotor of jets, helicopter blades, planets, acrobats, high divers, hurricanes, electrons, and atoms

    • Rotary Motion is all “around” us

Restrictions

  • Deal with only rigid bodies about a fixed axis

    • Not stars and the sun because not rigid

  • Rolling motion with moving axis not dealt with

  • Bowling ball because of changing axis

Rotational vs. Translational

  • Translational

    • Every point moves in a straight line

      • Fixed direction

    • Every point experiences linear displacement during a particular time interval

  • Rotational

    • Every point on the body moves around a circle whose center lies on the axis of motion

    • Every point experiences the same angular displacement during a particular time interval

Angular Position

  • Have to define angular position before talking about its motion

  • Use a reference line perpendicular to the axis of rotation

  • The position of an object can be described using polar coordinates rather than x and y

    • r - length measure from axis along reference line

    • θ - angle reference line makes to your original axis

Angular Measure

  • It is more convenient to measure the angle θ in radians

    • s = r * θ

Angular Displacement

  • Is the change in the angular position

    • Δθ = θf - θi

    • Can not be treated as a vector (unless very small)

      • To be a vector it must have magnitude and direction and follow rules for vector addition

      • Fails addition test

Angular Speed and Velocity

  • In analogy to the linear case, we define the average and instantaneous angular speed

  • Measured in rads/s, rev/s

  • Can be + or - depending on increasing θ or decreasing θ

    • Clockwise - negative

    • Counterclockwise - positive

  • The direction of the angular velocity is along the axis of rotation, and is given by a right-hand rule

Angular Acceleration

  • The average angular acceleration is the rate at which the angular speed changes

  • In analogy to constant linear acceleration

    • a = (ω - ω0) / t

    • ω = ω0 + a * t

  • Measured in:

    • rads/s², rev/s²