Chapter 7 review

    Match each word to the sentence where it best fits.
      Section 7.1

      angular velocity centripetal acceleration
      centripetal force radian (rad)
      1. _______ is expressed in radians per second.
      2. When measuring angles, the _______ is an alternative unit to a degree.
      3. The force that causes an object to move in a circle is the _______.
      4. Although acceleration usually causes a change in speed, _______ causes a change in direction.
      Section 7.2

      black hole escape velocity
      law of universal gravitation orbit
      orbital period satellite
      1. A consequence of Einstein’s theory of general relativity is that there can be a gravitational singularity called a/an _______.
      2. The Moon is the Earth’s natural _______.
      3. The _______ relates the two objects’ masses and the distance between them to how much they are attracted to each other.
      4. Many artificial satellites _______ the Earth and relay information across the globe.
      5. If you fire a rifle straight up in the air, the bullet will return to Earth because the bullet is not fired fast enough to exceed the Earth’s _______.
      6. It takes 687 Earth days for Mars to move once around the Sun. The _______ of Mars is therefore 687 days.
      Conceptual questions
        Section 7.1
        1. Ask two friends to tell you what a radian is. Compare their answers with your own understanding of radians. Did you learn anything new from your friends’ answers?
        2. Is a radian larger or smaller than a degree?
        1. Which of the following equations best represents the same meaning as the following sentence: “The angular velocity is the linear velocity divided by the radius of the motion.”
          1. v = ωr
          2. v = ω/r
          3. ω = v/r
          4. ω = r/v
        2. When a satellite orbits a planet in circles, its velocity is _______ to its orbit and its acceleration is _______ to its velocity.
          1. tangential, parallel
          2. parallel, perpendicular
          3. perpendicular, parallel
          4. tangential, perpendicular
        3. What are the units of angular velocity? Do these units have dimensions such as length, mass, or time?
        4. How does centripetal acceleration change when the radius decreases and the angular speed remains the same?
        5. What is the SI unit of angular frequency?
        6. Easy Imagine that you build a toy car. For it to work well, you want all four wheels to have the same linear velocity. (Otherwise, some will be trying to get ahead of the others!) Does this mean that all four wheels must have the same radius?
        7. Easy Which has a higher linear velocity when rolling, a big wheel or a small wheel with the same angular velocity?
        8. Easy A roller coaster car in an amusement park goes around a tight semi-circular turn. Describe the source and direction of the force that causes the car to move in a circular path.
        9. Easy Why are radians useful?
        10. Consider moving on a spiral path at constant speed
        11. Medium Say you are moving inward in a spiral at constant speed. Does the centripetal force needed for this increase or decrease as you move closer to the center?
        12. Medium Consider a purely centripetal force, such as gravity. If an object is moving in a circular path, does the centripetal force cause the object’s speed to change? Explain why or why not.

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