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Motion in a Circle - Physics with Calculus

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Termini in questo insieme (19)

  • Define angular displacement.
    The angle \(\theta\) through which an object moves from its starting position on a circle.
  • What is a radian?
    One radian is the angle subtended at the center of a circle by an arc equal in length to the radius.
  • How do you convert degrees to radians?
    Multiply degrees by \(\frac{\pi}{180}\) to get radians.
  • What is angular velocity \(\omega\)?
    The rate of change of angular displacement with respect to time.
  • How is linear speed related to angular velocity?
    Linear speed \(v\) equals radius \(r\) times angular velocity \(\omega\): \(v = r\omega\).
  • Why does velocity change in uniform circular motion despite constant speed?
    Because velocity is a vector, its direction changes continuously, making velocity change even if speed is constant.
  • What is centripetal force?
    A resultant force acting towards the center of the circle that causes centripetal acceleration.
  • What direction does centripetal force act relative to velocity?
    Centripetal force acts at right angles (perpendicular) to the object's velocity.
  • Does centripetal force do work on the object? Why or why not?
    No, because the force is perpendicular to displacement, so no work is done and kinetic energy remains constant.
  • List the conditions for uniform circular motion.
    1) Resultant force of constant magnitude, 2) Force normal to velocity, 3) Constant acceleration normal to velocity, 4) Constant angular speed.
  • What provides centripetal force for a car cornering on a level road?
    The frictional force between the tires and the road.
  • What provides centripetal force for a car on a banked road?
    The horizontal component of the normal force from the road surface.
  • What is centripetal acceleration?
    Acceleration directed towards the center of the circle, causing the change in velocity direction.
  • How does velocity and acceleration vary in vertical circular motion?
    Velocity and acceleration are maximum at the lowest point and minimum at the highest point of the circle.
  • Why does the tension in the string vary in vertical circular motion?
    Because gravity affects the net force needed for centripetal acceleration, tension changes with position.
  • What happens if centripetal acceleration is less than gravitational acceleration in vertical motion?
    The object will not stay on the circular path and may fall off the track.
  • What is the direction of the velocity vector in uniform circular motion?
    Tangential to the circular path at the object's position.
  • What is the direction of centripetal acceleration?
    Always directed towards the center of the circle.
  • Why is an object in uniform circular motion not in equilibrium?
    Because its velocity direction changes continuously, causing acceleration and requiring a resultant force.