2.10 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: a v r c 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 that are 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 velocity, 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: T f 1=
  • iii. For an object traveling at a constant speed in a circular path, the period is given by the derived equation

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 C: Mechanics does not expect students to know Kepler’s first or second laws of planetary motion.