Physics: Angular and Linear Velocity
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Physics: Angular and Linear Velocity

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Questions and Answers

What happens to the centripetal force if the radius of the circular motion is doubled while keeping speed constant?

  • The centripetal force stays the same.
  • The centripetal force quadruples.
  • The centripetal force is halved. (correct)
  • The centripetal force doubles.
  • In circular motion, how is centripetal acceleration related to angular velocity?

  • Centripetal acceleration increases with the square of angular velocity. (correct)
  • Centripetal acceleration is independent of angular velocity.
  • Centripetal acceleration is directly proportional to angular velocity.
  • Centripetal acceleration decreases as angular velocity increases.
  • What is the correct formula for calculating the centripetal force acting on an object in uniform circular motion?

  • F = mv²/r (correct)
  • F = mvr²
  • F = mrω
  • F = mω²r (correct)
  • Which of the following correctly describes the relationship between velocity, angular velocity, and radius?

    <p>Velocity is equal to angular velocity multiplied by radius.</p> Signup and view all the answers

    What is the direction of the centripetal force acting on an object moving in a circular path?

    <p>Towards the center of the circle.</p> Signup and view all the answers

    What is the correct relationship between period of rotation and frequency?

    <p>Frequency is the inverse of the period of rotation.</p> Signup and view all the answers

    To convert an angle of 180° to radians, which formula correctly applies?

    <p>Multiply by $ rac{2 ext{π}}{360}$</p> Signup and view all the answers

    What does angular velocity represent in terms of circular motion?

    <p>The rate of change of angular displacement.</p> Signup and view all the answers

    Which of the following statements regarding radians is true?

    <p>Radian measure is based on the arc length being equal to the radius.</p> Signup and view all the answers

    In circular motion, how is the direction of angular velocity defined?

    <p>It can be positive or negative based on the defined rotational direction.</p> Signup and view all the answers

    Study Notes

    Circular Motion Concepts

    • Velocity in circular motion can be expressed as ( v = \omega r ), where ( \omega ) is the angular velocity in radians per second and ( r ) is the radius.
    • The arc length traveled in one second equals the product of angular velocity and radius.

    Centripetal Force

    • Centripetal force is the resultant force acting on an object in uniform circular motion, directed towards the center of the circle.
    • Formula for centripetal force: ( F = \frac{mv^2}{r} ) or ( F = mw^2 r ), where ( m ) is mass, ( v ) is velocity, and ( r ) is the radius of the circle.

    Centripetal Acceleration

    • Centripetal acceleration is always directed towards the center of the circle, proportional to the resultant force according to Newton’s second law.
    • Formula for centripetal acceleration: ( a = \frac{v^2}{r} ) or ( a = w^2 r ).

    Definitions

    • Period of Rotation: Time taken for one complete revolution in circular motion.
    • Frequency: Number of complete rotations or oscillations per unit time.
    • Radian: An angle measure where one radian is the angle subtended by an arc length equal to the radius.

    Angular Conversion

    • There are ( 2\pi ) radians in a complete circle (360°).
    • To convert radians to degrees: ( \text{degrees} = \frac{\text{radians} \times 360}{2\pi} ).
    • To convert degrees to radians: ( \text{radians} = \frac{\text{degrees} \times 2\pi}{360} ).

    Angular Velocity

    • Angular velocity (( \omega )) measures the rate of change of angular displacement and is a vector quantity.
    • Its sign indicates direction (positive for counter-clockwise, negative for clockwise).
    • In simple harmonic motion, the relation between angular velocity and frequency is given by ( \omega = 2\pi f ).
    • Circular motion exhibits simple harmonic motion characteristics when viewed from the side, illustrating a connection between the two concepts.

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    Description

    Explore the relationship between linear velocity and angular velocity through the equation v = ωr. This quiz covers the basic geometric principles of circles and how they define motion in terms of both angular and linear measurements.

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