2.9 Circular Motion

Describe the motion of an object traveling in a circular path.

• Centripetal acceleration is the component of an object’s acceleration directed toward the center of the object’s circular path.
  • i. The magnitude of centripetal acceleration for an object moving in a circular path is the ratio of the object’s tangential speed squared to the radius of the circular path. Relevant equation: =av rc 2
  • ii. Centripetal acceleration is directed toward the center of an object’s circular path.
• Centripetal acceleration can result from a single force, more than one force, or components of forces exerted on an object in circular motion.
  • i. At the top of a vertical, circular loop, an object requires a minimum speed to maintain circular motion. At this point, and with this minimum speed, the gravitational force is the only force that causes the centripetal acceleration. Derived equation: =vg r
  • ii. Components of the static friction force and the normal force can contribute to the net force producing centripetal acceleration of an object traveling in a circle on a banked surface.
  • iii. A component of tension contributes to the net force producing centripetal acceleration experienced by a conical pendulum.
• T angential acceleration is the rate at which an object’s speed changes and is directed tangent to the object’s circular path.
• The net acceleration of an object moving in a circle is the vector sum of the centripetal acceleration and tangential acceleration.
• The revolution of an object traveling in a circular path at a constant speed (uniform circular motion) can be described using period and frequency.
  • i. The time to complete one full circular path, one full rotation, or a full cycle of oscillatory motion is defined as period, T.
  • ii. The rate at which an object is completing revolutions is defined as frequency, f. Relevant equation: =Tf 1
  • iii. For an object traveling at a constant speed in a circular path, the period is given by the derived equation AP Physics 1: Algebra-Based Course and Exam Description Force and Translational Dynamics UNIT 2

Describe circular orbits using Kepler’s third law.

• For a satellite in circular orbit around a central body, the satellite’s centripetal acceleration is caused only by gravitational attraction. The period and radius of the circular orbit are related to the mass of the central body. Derived equation: BOUNDARY STATEMENT AP Physics 1 only expects students to quantitatively analyze banked curves in which no friction is required to maintain uniform circular motion. Analysis of situations in which friction is required on a banked curve is limited to qualitative descriptions. BOUNDARY STATEMENT AP Physics 1 does not expect students to know Kepler’s first or second laws of planetary motion. AP Physics 1: Algebra-Based Course and Exam Description AP PHYSICS 18–23% AP EXAM WEIGHTING ~22–27 CLASS PERIODS 59 | AP Physics 1: Algebra-Based Course and Exam Description Remember to go to AP Classroom to assign students the online Progress Check for this unit. Whether assigned as homework or completed in class, the Progress Check provides each student with immediate feedback related to this unit’s topics and science practices. Progress Check 3 Multiple-choice: ~18 questions Free-response: 4 questions