AP®PhysicsCollege BoardPhysics 1: Algebra-BasedStudy GuidesUnit 5: Torque & Rotational DynamicsRotational KinematicsRotational Kinematics Graphs

Rotational Kinematics Graphs (College Board AP® Physics 1: Algebra-Based)

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Katie M

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Katie M

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Rotational kinematics graphs

  • Graphs of angular displacement, angular velocity, and angular acceleration as functions of time can be used to find the relationships between those quantities

  • These graphs can be interpreted in the same way as graphs of linear motion

Graphical representation of angular displacement, velocity, and acceleration against time, showing gradients and areas under curves representing relationships between these quantities.
Graphs of angular displacement, angular velocity and angular acceleration

Angular position-versus-time graphs

  • Angular position-versus-time graphs are used to show the change in angular position or angular displacement of a system over time

  • On an angular position-versus-time graph:

    • the slope equals the angular velocity

    • the area under the curve doesn't represent anything

    • the y-intercept equals the initial angular position

    • a constant slope represents a constant angular velocity

    • a curved line represents an angular acceleration

    • a positive slope represents angular velocity in the positive direction

    • a negative slope represents angular velocity in the negative direction

    • a zero slope (horizontal line) represents a state of rest (no rotation)

Three graphs comparing angular position versus time, labeled: constant angular velocity (linear), constant angular acceleration (quadratic), and increasing angular acceleration (exponential).
Constant angular velocity, constant angular acceleration, and increasing angular acceleration on an angular position-versus-time graph

Angular velocity-versus-time graphs

  • Angular velocity-versus-time graphs are used to show the change in angular velocity of a system over time

  • On an angular velocity-versus-time graph:

    • the slope equals angular acceleration

    • the area under the curve is equal to the angular displacement

    • the y-intercept equals the initial angular velocity

    • a constant slope represents constant angular acceleration

    • a curve represents non-constant angular acceleration

    • a positive slope represents angular acceleration in the positive direction

    • a negative slope represents angular acceleration in the negative direction

    • a zero slope (horizontal line) represents constant angular velocity

Three angular velocity-time graphs showing constant angular velocity as a horizontal line, constant angular acceleration as a constant slope, and increasing angular acceleration as an upward curve with labeled axes for angular velocity and time.
Constant angular velocity, constant angular acceleration, and increasing angular acceleration on an angular velocity-versus-time graph

Angular acceleration-versus-time graphs

  • Angular acceleration-versus-time graphs are used to show the change in the acceleration of an object over time

  • On an angular acceleration-versus-time graph:

    • the slope doesn't represent anything

    • the area under the curve equals the change in angular velocity

    • the y-intercept equals the initial angular acceleration

    • a zero slope (horizontal line) represents constant angular acceleration

Three angular acceleration vs time graphs: flat line at zero for constant angular velocity, flat line above zero for constant angular acceleration, and a positive slope line for increasing angular acceleration.
Constant angular velocity, constant angular acceleration, and increasing angular acceleration on an angular acceleration-versus-time graph

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.