centripetal
(adjective)
Directed or moving towards a center.
Examples of centripetal in the following topics:
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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).
- A force that causes motion in a curved path is called a centripetal force.
- Uniform circular motion is an example of centripetal force in action.
- Centripetal force can also be expressed in terms of angular velocity.
- The equation for centripetal force using angular velocity is:
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Kinematics of UCM
- Any force or combination of forces can cause a centripetal or radial acceleration.
- Any net force causing uniform circular motion is called a centripetal force.
- 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: $a = a_c$.
- Thus, the magnitude of centripetal force $F_c$ is:
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Centripetial Acceleration
- Centripetal acceleration is the constant change in velocity necessary for an object to maintain a circular path.
- 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.
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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.
- 2: The radial (centripetal) force is constant (like a satellite rotating about the earth under the influence of a constant force of gravity).
- In any eventuality, the equation of centripetal acceleration in terms of "speed" and "radius" must be satisfied.
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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.
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Circular Motion
- An object in circular motion undergoes acceleration due to centripetal force in the direction of the center of rotation.
- 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.
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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.
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Banked and Unbacked Highway Curves
- For ideal banking, the net external force equals the horizontal centripetal force in the absence of friction.
- The components of the normal force $N$ in the horizontal and vertical directions must equal the centripetal force and the weight of the car, respectively.
- Only the normal force has a horizontal component, and so this must equal the centripetal force—that is:
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Energy of a Bohr Orbit
- We start by noting the centripetal force causing the electron to follow a circular path is supplied by the Coulomb force.
- The magnitude of the centripetal force is $\frac{m_ev^2}{r_n}$, while the Coulomb force is $\frac{Zk_e e^2}{r^2}$.
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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