Goal: Unit 5 reinforces the Unit 2 ideas of force and linear motion by introducing students to their rotational analogs—torque and rotational motion. Although these topics present more complex scenarios, the tools of analysis remain the same. The content and models explored in the first four units of the course set the foundation for Units 5 and 6. During their study of torque and rotational motion, students will be introduced to different ways of modeling forces. Throughout Units 5 and 6, students will compare and connect their understanding of linear and rotational motion, dynamics, energy, and momentum to develop holistic models to evaluate physical phenomena.
To access the main folder and get class notes and additional practice problems per each topic below click the following link:
AP Physics 1-Unit 5-Torque and Rotational Dynamics
(time to complete all WebAssign Problems approximately 7hr 15min)
**We will be starting this Unit BEFORE Midterm Exam, but will not be tested on the Midterm Exam. You will take 1 test during this unit.**
Learning Objective:
-Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration.
Essential Knowledge:
-Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration
-Describe the rotation of a system with respect to time using angular displacement, angular velocity, and angular acceleration.
-A rigid system cannot be modeled as an object.
-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.
-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.
-Average angular acceleration is the average rate at which the angular velocity changes with respect to time.
-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.
-For constant angular acceleration, the mathematical relationship exist between angular displacement, angular velocity, and angular acceleration.
-Graphs of angular displacement, angular velocity, and angular acceleration as functions of time can be used to find the relationships between those quantities.
Skills:
-Create quantitative graphs with appropriate scales and units, including plotting data.
-Derive a symbolic expression from known quantities by selecting and following a logical mathematical pathway.
-Predict new values or factors of change of physical quantities using functional dependence between variables.
-Create experimental procedures that are appropriate for a given scientific question.
-Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.
Read & Take Notes on Sections: 7.1, 7.2
WebAssign: Ch7 - 1, 2, 3, 4
Learning Objective:
-Describe the linear motion of a point on a rotating rigid system that corresponds to the rotational motion of that point, and vice versa.
Essential Knowledge:
-For a point at a distance r from a fixed axis of rotation, the linear distance s traveled by the point as the system rotates through an angle is given by the equation s = r(θ).
-Derived relationships of linear velocity and of the tangential component of acceleration to their respective angular quantities are given by the following equations: s = r(θ), v = r(θ), a = r(θ)
-For a rigid system, all points within that system have the same angular velocity and angular acceleration.
Skills:
-Create qualitative sketches of graphs that represent features of a model or the behavior of a physical system.
-Derive a symbolic expression from known quantities by selecting and following a logical mathematical pathway.
-Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 7.3
WebAssign: Ch7 - 5, 9, 10, 12, 16, 17
Learning Objective:
-Identify the torques exerted on a rigid system.
-Describe the torques exerted on a rigid system.
Essential Knowledge:
-Torque results only from the force component perpendicular to the position vector from the axis of rotation to the point of application of the force.
-The lever arm is the perpendicular distance from the axis of rotation to the line of action of the exerted force.
-Torques can be described using force diagrams.
-Force diagrams are similar to free-body diagrams and are used to analyze the torques exerted on a rigid system.
-Similar to free-body diagrams, force diagrams represent the relative magnitude and direction of the forces exerted on a rigid system. Force diagrams also depict the location at which those forces are exerted relative to the axis of rotation.
-The magnitude of the torque exerted on a rigid system by a force can be calculated.
Skills:
-Create diagrams, tables, charts, or schematics to represent physical situations.
-Derive a symbolic expression from known quantities by selecting and following a logical mathematical pathway.
-Predict new values or factors of change of physical quantities using functional dependence between variables.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 8.1, 8.3, 8.4
WebAssign: Ch8 - 1, 2, 3, 18, 19, 21, 27, 34, 46, 94
Learning Objective:
-Describe the rotational inertia of a rigid system relative to a given axis of rotation.
-Describe the rotational inertia of a rigid system rotating about an axis that does not pass through the system’s center of mass.
Essential Knowledge:
-Rotational inertia measures a rigid system’s resistance to changes in rotation and is related to the mass of the system and the distribution of that mass relative to the axis of rotation.
-The rotational inertia of an object rotating a perpendicular distance r from an axis is described by the equation I = mr2.
-The total rotational inertia of a collection of objects about an axis is the sum of the rotational inertias of each object about that axis.
-A rigid system’s rotational inertia in a given plane is at a minimum when the rotational axis passes through the system’s center of mass.
NOT IN TEXTBOOK -The parallel axis theorem relates the rotational inertia of a rigid system about any axis that is parallel to an axis through its center of mass.
Skills:
-Create quantitative graphs with appropriate scales and units, including plotting data.
-Calculate or estimate an unknown quantity with units from known quantities, by selecting and following a logical computational pathway.
-Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
-Create experimental procedures that are appropriate for a given scientific question.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 8.4
Video: Parallel Axis Theorem Derivation
WebAssign: Ch8 - 37, 41
**Note**
-Students expected to calculate the rotational inertia for systems of five or fewer objects arranged in a two-dimensional configuration.
-Students do not need to know the rotational inertia of extended rigid systems, as these will be provided within the exam.
-Students should have a qualitative understanding of the factors that affect rotational inertia; for example, how rotational inertia is greater when mass is farther from the axis of rotation, which is why a hoop has more rotational inertia than a solid disk of the same mass and radius.
Learning Objective:
-Describe the conditions under which a system’s angular velocity remains constant.
Essential Knowledge:
-A system may exhibit rotational equilibrium (constant angular velocity) without being in translational equilibrium, and vice versa.
-Free-body and force diagrams describe the nature of the forces and torques exerted on an object or rigid system.
-Rotational equilibrium is a configuration of torques such that the net torque exerted on the system is zero.
-The rotational analog of Newton’s first law is that a system will have a constant angular velocity only if the net torque exerted on the system is zero.
-A rotational corollary to Newton’s second law states that if the torques exerted on a rigid system are not balanced, the system’s angular velocity must be changing.
Skills:
-Create qualitative sketches of graphs that represent features of a model or the behavior of a physical system.
-Derive a symbolic expression from known quantities by selecting and following a logical mathematical pathway.
-Calculate or estimate an unknown quantity with units from known quantities, by selecting and following a logical computational pathway.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 8.4
WebAssign: Ch8 - 37, 41
Learning Objective:
-Describe the conditions under which a system’s angular velocity changes.
Essential Knowledge:
-Angular velocity changes when the net torque exerted on the object or system is not equal to zero.
-The rate at which the angular velocity of a rigid system changes is directly proportional to the net torque exerted on the rigid system and is in the same direction. The angular acceleration of the rigid system is inversely proportional to the rotational inertia of the rigid system.
-To fully describe a rotating rigid system, linear and rotational analyses may need to be performed independently.
Skills:
-Create diagrams, tables, charts, or schematics to represent physical situations.
-Derive a symbolic expression from known quantities by selecting and following a logical mathematical pathway.
-Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
-Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.
Read & Take Notes on Sections: 8.4
WebAssign: Ch8 - 39, 46, 47 & Ch8 AP Multiple-Choice Review Questions
Test #7