Classical mechanicsLesson 3 of 4 in the course Applications of Newton's Laws

Circular Motion, Banked Turns, and Rotating Frames

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Circular motion requires an object’s velocity to change direction, even when its speed stays constant. This lesson connects that change in direction to centripetal acceleration and the net force that produces it.

Velocity is a vector: it has both magnitude and direction. In uniform circular motion, speed is constant, but the direction of velocity changes continuously. A change in velocity means there is acceleration. This acceleration points toward the center of the circular path and is called centripetal acceleration or radial acceleration.

All flashcards

Why is circular motion accelerated even at constant speed?
Velocity includes direction as well as magnitude. In circular motion, direction changes continuously, so velocity changes and acceleration is present even when speed is constant.
What is centripetal acceleration?
The inward, center-directed acceleration of an object following a curved or circular path. Its magnitude is ac=v2/ra_c=v^2/r or, using angular velocity, ac=rω2a_c=r\omega^2.
What is the direction of velocity in circular motion?
At each instant, velocity points along the tangent to the path. It is perpendicular to the inward centripetal acceleration.
Define centripetal force.
Centripetal force is the inward net force that produces centripetal acceleration. Its magnitude is Fc=mac=mv2/r=mrω2F_c=ma_c=mv^2/r=mr\omega^2.
Is centripetal force a distinct physical interaction?
No. It describes the role of the net inward force, which can be provided by actual forces such as tension, gravity, friction, or a normal force.

Quiz questions

  1. In the ideal frictionless banked-curve model, what determines the required bank angle for a given speed and radius?Answer: The angle is independent of the vehicle's mass.
  2. On an ideal frictionless banked curve, which force component supplies the inward centripetal force?Answer: The horizontal component of the normal force.
  3. How does a banked airplane obtain the inward force needed to turn?Answer: The horizontal component of lift points toward the turn's center.
  4. How is centrifugal force interpreted when analyzing motion from an inertial frame?Answer: It is not a physical outward force in that frame.
  5. Viewed from above the North Pole, how does Earth's rotation deflect moving objects in the Northern Hemisphere?Answer: Toward the right of their direction of motion.

Based on University Physics Volume 1 by William Moebs, Samuel J. Ling, Jeff Sanny (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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