AP®︎ Physics 1: Topic 5.1 Practice Test

Essential Knowledge: 5.1.A.1

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: $\Delta\theta = \theta - \theta_0$

Essential Knowledge: 5.1.A.1.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.

Essential Knowledge: 5.1.A.1.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.

Essential Knowledge: 5.1.A.1.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.

Essential Knowledge: 5.1.A.2

Average angular velocity is the average rate at which angular position changes with respect to time. Relevant equation: $\omega_{\mathrm{avg}} = \frac{\Delta\theta}{\Delta t}$

Essential Knowledge: 5.1.A.3

Average angular acceleration is the average rate at which the angular velocity changes with respect to time. Relevant equation: $\alpha_{\mathrm{avg}} = \frac{\Delta\omega}{\Delta t}$

Essential Knowledge: 5.1.A.4

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.

Essential Knowledge: 5.1.A.4.i

For constant angular acceleration, the mathematical relationships between angular displacement, angular velocity, and angular acceleration can be described with the following equations: $\omega = \omega_0 + \alpha t$; $\theta = \theta_0 + \omega_0t + \frac{1}{2}\alpha t^2$; $\omega^2 = \omega_0^2 + 2\alpha(\theta - \theta_0)$

Essential Knowledge: 5.1.A.4.ii

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