5.1.A—Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular…

Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration. BOUNDARY STATEMENT Descriptions of the directions of rotation for a point or object are limited to clockwise and counterclockwise with respect to a given axis of rotation. AP Physics 1: Algebra-Based Course and Exam Description Torque and Rotational Dynamics UNIT 5 TOPIC 5.2 Connecting Linear and Rotational Motion

• Angular displacement is the measurement of the angle, in radians, through which a point on a rigid system rotates about a specified axis. Relevant equation:
  • i. A rigid system is one that holds its shape but in which different points on the system move in different directions during rotation. A rigid system cannot be modeled as an object.
  • ii. One direction of angular displacement about an axis of rotation—clockwise or counterclockwise—is typically indicated as mathematically positive, with the other direction becoming mathematically negative.
  • iii. If the rotation of a system about an axis may be well described using the motion of the system’s center of mass, the system may be treated as a single object. For example, the rotation of Earth about its axis may be considered negligible when considering the revolution of Earth about the center of mass of the Earth–Sun system.
• Average angular velocity is the average rate at which angular position changes with respect to time. Relevant equation:
• Average angular acceleration is the average rate at which the angular velocity changes with respect to time. Relevant equation:
• Angular displacement, angular velocity, and angular acceleration around one axis are analogous to linear displacement, velocity, and acceleration in one dimension and demonstrate the same mathematical relationships.
  • i. For constant angular acceleration, the mathematical relationships between angular displacement, angular velocity, and angular acceleration can be described with the following equations:
  • ii. Graphs of angular displacement, angular velocity, and angular acceleration as functions of time can be used to find the relationships between those quantities.