centripetal acceleration

Examples of centripetal acceleration in the following topics:

• Centripetial Acceleration

  • Centripetal acceleration is the constant change in velocity necessary for an object to maintain a circular path.
  • This feeling is an acceleration.
  • To calculate the centripetal acceleration of an object undergoing uniform circular motion, it is necessary to have the speed at which the object is traveling and the radius of the circle about which the motion is taking place.
  • The centripetal acceleration may also be expressed in terms of rotational velocity as follows:
  • A brief overview of centripetal acceleration for high school physics students.

• Angular Acceleration, Alpha

  • In circular motion, centripetal acceleration, ac, refers to changes in the direction of the velocity but not its magnitude.
  • An object undergoing circular motion experiences centripetal acceleration (as seen in the diagram below.)
  • Centripetal acceleration occurs as the direction of velocity changes; it is perpendicular to the circular motion.
  • Centripetal and tangential acceleration are thus perpendicular to each other.
  • This acceleration is called tangential acceleration.

• Kinematics of UCM

  • The acceleration can be written as:
  • This acceleration, responsible for the uniform circular motion, is called centripetal acceleration.
  • Any force or combination of forces can cause a centripetal or radial acceleration.
  • The direction of a centripetal force is toward the center of curvature, the same as the direction of centripetal acceleration.
  • For uniform circular motion, the acceleration is the centripetal acceleration: $a = a_c$.

• Overview of Non-Uniform Circular Motion

  • The change in direction is accounted by radial acceleration (centripetal acceleration), which is given by following relation: $a_r = \frac{v^2}{r}$.
  • The change in speed has implications for radial (centripetal) acceleration.
  • This means that the centripetal acceleration is not constant, as is the case with uniform circular motion.
  • In any eventuality, the equation of centripetal acceleration in terms of "speed" and "radius" must be satisfied.
  • The important thing to note here is that, although change in speed of the particle affects radial acceleration, the change in speed is not affected by radial or centripetal force.

• Centripetal Force

  • A force which causes motion in a curved path is called a centripetal force (uniform circular motion is an example of centripetal force).
  • Previously, we learned that any change in a velocity is an acceleration.
  • As the object moves through the circular path it is constantly changing direction, and therefore accelerating—causing constant force to be acting on the object.
  • From Newton's second law $F= m \cdot a$, we can see that centripetal acceleration is:
  • As an object travels around a circular path at a constant speed, it experiences a centripetal force accelerating it toward the center.

• Simple Harmonic Motion and Uniform Circular Motion

  • This varying velocity indicates the presence of an acceleration called the centripetal acceleration.
  • Centripetal acceleration is of constant magnitude and directed at all times towards the center of the circle.
  • This acceleration is, in turn, produced by a centripetal force—a force in constant magnitude, and directed towards the center.
  • The acceleration points radially inwards (centripetally) and is perpendicular to the velocity.
  • This acceleration is known as centripetal acceleration.

• Winds

  • At the surface of the star we know that the centripetal acceleration must be less than the gravitational acceleration, so
  • The ratio of the centripetal acceleration to the gravitational acceleration decreases as

• Accretion Disks

  • If the material conserves angular momentum we can compare the centripetal acceleration with gravitational acceleration to give

• Circular Motion

  • An object in circular motion undergoes acceleration due to centripetal force in the direction of the center of rotation.
  • Since the velocity vector of the object is changing, an acceleration is occurring.
  • For this reason, acceleration in uniform circular motion is recognized to "seek the center" -- i.e., centripetal force.
  • In uniform circular motion, the centripetal force is perpendicular to the velocity.
  • The centripetal force points toward the center of the circle, keeping the object on the circular track.

• Examples and Applications

  • A cyclotron is a type of particle accelerator in which charged particles accelerate outwards from the center along a spiral path.
  • This frequency is given by equality of centripetal force and magnetic Lorentz force.
  • The particles accelerated by the cyclotron can be used in particle therapy to treat some types of cancer.
  • The synchrotron is one of the first accelerator concepts that enable the construction of large-scale facilities, since bending, beam focusing and acceleration can be separated into different components.
  • Sketch of a particle being accelerated in a cyclotron, and being ejected through a beamline.