There are, in fact, precise rotational analogs to both force and mass.įigure 10.10 Force is required to spin the bike wheel. These relationships should seem very similar to the familiar relationships among force, mass, and acceleration embodied in Newton's second law of motion. The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration another implication is that angular acceleration is inversely proportional to mass. Furthermore, we know that the more massive the door, the more slowly it opens. For example, we know that a door opens slowly if we push too close to its hinges. In fact, your intuition is reliable in predicting many of the factors that are involved. If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in Figure 10.10. Students are expected to do calculations with a fixed set of extended objects and point masses. Students are expected to do qualitative reasoning with compound objects. 5.E.2.1 The student is able to describe or calculate the angular momentum and rotational inertia of a system in terms of the locations and velocities of objects that make up the system.

4.D.1.2 The student is able to plan data collection strategies designed to establish that torque, angular velocity, angular acceleration, and angular momentum can be predicted accurately when the variables are treated as being clockwise or counterclockwise with respect to a well-defined axis of rotation, and refine the research question based on the examination of data.4.D.1.1 The student is able to describe a representation and use it to analyze a situation in which several forces exerted on a rotating system of rigidly connected objects change the angular velocity and angular momentum of the system.The information presented in this section supports the following AP® learning objectives and science practices:

Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.

Understand the relationship between force, mass, and acceleration.

By the end of this section, you will be able to do the following:

Whole body moment of inertia equation