6.3 Angular Momentum and Angular Impulse

Describe the angular momentum of an object or rigid system.

• The magnitude of the angular momentum of a rigid system about a specific axis can be described with the equation
• The magnitude of the angular momentum of an object about a given point is
  • i. The selection of the axis about which an object is considered to rotate influences the determination of the angular momentum of that object.
  • ii. 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.

Describe the angular impulse delivered to an object or rigid system by a torque.

• 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. Relevant equation: angulari mpulse
• 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.

Relate an object’s or rigid system’s change in angular momentum to the angular impulse given to that object or rigid system. BOUNDARY STATEMENT 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. AP Physics 1: Algebra-Based Course and Exam Description Energy and Momentum of Rotating Systems UNIT 6 TOPIC 6.4 Conservation of Angular Momentum

• 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.
  • i. The angular impulse exerted on an object or rigid system is equal to the change in angular momentum of that object or rigid system. Relevant equation:
  • ii. 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:
• 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.