Goal: Students will apply their knowledge of energy and momentum to rotating systems. Similar to the approach used for translational energy and momentum concepts in Units 3 and 4, it is important that students have conceptual understanding of how angular momentum and rotational energy change due to external torque(s) on a system. Additionally, articulating the conditions under which the rotational energy and/or angular momentum of a system remains constant is foundational to working through more complex scenarios. Students will use the content and skills presented in both Units 5 and 6 to further study the motion of orbiting satellites and rolling without slipping in this unit.
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 6-Energy and Momentum of Rotating Systems
(time to complete all WebAssign Problems approximately 5hr 08min)
**You will take 1 test during this unit.**
Learning Objective:
-Describe the rotational kinetic energy of a rigid system in terms of the rotational inertia and angular velocity of that rigid system.
Essential Knowledge:
-The rotational kinetic energy of an object or rigid system is related to the rotational inertia and angular velocity of the rigid system.
-The rotational inertia of an object about a fixed axis can be used to show that the rotational kinetic energy of that object is equivalent to its translational kinetic energy, which is its total kinetic energy.
-The total kinetic energy of a rigid system is the sum of its rotational kinetic energy due to its rotation about its center of mass and the translational kinetic energy due to the linear motion of its center of mass.
-A rigid system can have rotational kinetic energy while its center of mass is at rest due to the individual points within the rigid system having linear speed and, therefore, kinetic energy.
-Rotational kinetic energy is a scalar quantity.
Skills:
-Create diagrams, tables, charts, or schematics to represent physical situations.
-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.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 8.5
WebAssign: Ch8 - 48, 49, 50, 52, 54, 55, 58
Learning Objective:
-Describe the work done on a rigid system by a given torque or collection of torques.
Essential Knowledge:
-A torque can transfer energy into or out of an object or rigid system if the torque is exerted over an angular displacement.
-The amount of work done on a rigid system by a torque is related to the magnitude of that torque and the angular displacement through which the rigid system rotates during the interval in which that torque is exerted.
-Work done on a rigid system by a given torque can be found from the area under the curve of a graph of torque as a function of angular position.
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.
-Compare physical quantities between two or more scenarios or at different times and locations in a single scenario.
-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.
Read & Take Notes on Sections:
Video: Rotational Power, Work, Energy, Torque & Moment of Inertia - Physics Problems
WebAssign:
Learning Objective:
-Describe the angular momentum of an object or rigid system.
-Describe the angular impulse delivered to an object or rigid system by a torque.
-Relate an object’s or rigid system’s change in angular momentum to the angular impulse given to that object or rigid system.
Essential Knowledge:
-The magnitude of the angular momentum of a rigid system about a specific axis can be described as the product between rotational inertia and rotational velocity.
-The magnitude of the angular momentum of an object about a given point is L = rmv sin(θ).
-The selection of the axis about which an object is considered to rotate influences the determination of the angular momentum of that object.
-The measured angular momentum of an object traveling in a straight line depends on the distance between the reference point and the object, the mass of the object, the speed of the object, and the angle between the radial distance and the velocity of the object.
-Angular impulse is defined as the product of the torque exerted on an object or rigid system and the time interval during which the torque is exerted.
-Angular impulse has the same direction as the torque exerted on the object or system.
-The angular impulse delivered to an object or rigid system by a torque can be found from the area under the curve of a graph of the torque as a function of time.
-The magnitude of the change in angular momentum can be described by comparing the magnitudes of the final and initial angular momenta of the object or rigid system.
-A rotational form of the impulse–momentum theorem relates the angular impulse delivered to an object or rigid system and the change in angular momentum of that object or rigid system.
-The angular impulse exerted on an object or rigid system is equal to the change in angular momentum of that object or rigid system.
-The rotational form of the impulse–momentum theorem is a direct result of the rotational form of Newton’s second law of motion for cases in which rotational inertia is constant.
-Relate the change in angular momentum of an object or rigid system to the angular impulse given to that object or rigid system.
-The net torque exerted on an object is equal to The slope of The graph of The angular momentum of an object as a function of time.
-The angular impulse delivered to an object is equal to the area under the curve of a graph of the net external torque exerted on an object as a function of time.
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.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
Read & Take Notes on Sections: 8.6; Angular Impulse is not in the textbook
WebAssign: Ch8 - 60, 64, 70, 73; No angular Impulse problems at this time
Videos: Angular Momentum-right hand rule ;Gyroscopic Precession
**Note**
-While AP Physics 1 expects that students can mathematically manipulate the magnitude of angular momentum using one-dimensional vector conventions, the direction of angular momentum and angular impulse is beyond the scope of the course.
Learning Objective:
-Describe the behavior of a system using conservation of angular momentum.
-Describe how the selection of a system determines whether the angular momentum of that system changes.
Essential Knowledge:
-The total angular momentum of a system about a rotational axis is the sum of the angular momenta of the system’s constituent parts about that axis.
-Any change to a system’s angular momentum must be due to an interaction between the system and its surroundings.
-The angular impulse exerted by one object or system on a second object or system is equal and opposite to the angular impulse exerted by the second object or system on the first. This is a direct result of Newton’s third law.
-A system may be selected so that the total angular momentum of that system is constant.
-The angular speed of a nonrigid system may change without The angular momentum of The system changing if The system changes shape by moving mass closer to or further from the rotational axis.
-If the total angular momentum of a system changes, that change will be equivalent to the angular impulse exerted on the system.
-Angular momentum is conserved in all interactions.
-If the net external torque exerted on a selected object or rigid system is zero, the total angular momentum of that system is constant.
-If the net external torque exerted on a selected object or rigid system is nonzero, angular momentum is transferred between the system and the environment.
Skills:
-Create quantitative graphs with appropriate scales and units, including plotting data.
-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.
-Apply an appropriate law, definition, theoretical relationship, or model to make a claim.
-Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.
Read & Take Notes on Sections: 8.6
WebAssign: Ch8 - 60, 64, 65, 66, 70, 73
Learning Objective:
-Describe the kinetic energy of a system that has translational and rotational motion.
-Describe the motion of a system that is rolling without slipping.
-Describe the motion of a system that is rolling while slipping.
Essential Knowledge:
-The total kinetic energy of a system is the sum of the system’s translational and rotational kinetic energies.
-While rolling without slipping, the translational motion of a system’s center of mass is related to the rotational motion of the system itself with the equations: scm = r(θ), vcm = r(θ), acm = r(θ)
-For ideal cases, rolling without slipping implies that the frictional force does not dissipate any energy from the rolling system.
-When slipping, the motion of a system’s center of mass and the system’s rotational motion cannot be directly related.
-When a rotating system is slipping relative to another surface, the point of application of the force of kinetic friction exerted on the system moves with respect to the surface, so the force of kinetic friction will dissipate energy from the system.
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: 8.5
WebAssign: Ch8 - 52, 57
**Note**
-Rolling friction is beyond the scope of AP Physics 1.
-Students are expected to qualitatively explain The changes to linear and angular quantities while a rigid body is rolling while slipping, but NOT quantitatively explain.
Learning Objective:
-Describe the motions of a system consisting of two objects interacting only via gravitational forces.
Essential Knowledge:
-In a system consisting only of a massive central object and an orbiting satellite with mass that is negligible in comparison to the central object’s mass, the motion of the central object itself is negligible.
-The motion of satellites in orbits is constrained by conservation laws.
-In circular orbits, the system’s total mechanical energy, the system’s gravitational potential energy, and the satellite’s angular momentum and kinetic energy are constant.
-In elliptical orbits, the system’s total mechanical energy and the satellite’s angular momentum are constant, but the system’s gravitational potential energy and the satellite’s kinetic energy can each change.
-The gravitational potential energy of a system consisting of a satellite and a massive central object is defined to be zero when the satellite is an infinite distance from the central object.
-The escape velocity of a satellite is the satellite’s velocity such that the mechanical energy of the satellite–central-object system is equal to zero.
-When the only force exerted on a satellite is gravity from a central object, a satellite that reaches escape velocity will move away from the central body until its speed reaches zero at an infinite distance from the central body.
-The escape velocity of a satellite from a central body of mass M can be derived using conservation of energy laws.
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.
-Justify or support a claim using evidence from experimental data, physical representations, or physical principles or laws.
Read & Take Notes on Sections: 7.5, 8.6
WebAssign: Ch8 - 60, 64, 65 & Ch7 41, 46; Problems dealing with satellites to follow & Ch8 AP Multiple-Choice Review Questions
Test #8