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

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