Mathematics of Circular Motion



Mathematics of Circular Motion

Read from Lesson 2 of the Circular and Satellite Motion chapter at The Physics Classroom:







MOP Connection: Circular Motion and Gravitation: CG5

The verbal descriptions of physical situations and the corresponding free-body diagrams are given below. Use your understanding of Newton's laws and centripetal force to fill in the blanks.

|Free Body Diagram |Show your work or justify your answer |

|1. A 900-kg car is doing donuts in a parking lot with a 32-m | |

|diameter. The car does 10 revolutions in 80 seconds. |Fnorm: |

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| |Ffrict: |

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| |Fgrav: |

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| |v: |

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| |a: |

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| |Fnet: |

|2. A bucket of water (m=2.0 kg) is attached to a 0.80-m long string | |

|and spun in a vertical circle. The speed of the water at the bottom |Ftens: |

|of the circular path is 6.0 m/s. | |

|[pic] | |

| |Fgrav: |

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| |a: |

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| |Fnet: |

|3. A 500-kg roller coaster car is at the top of the loop on the | |

|Shockwave. The radius of the loop is 4.0 m and the speed is 8.0 m/s. |Fgrav: |

|[pic] | |

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| |Fnorm: |

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| |a: |

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| |Fnet: |

4. An object is moving in a circle and experiences centripetal acceleration. Sometime later, the velocity is doubled while the radius stays the same. What happens to the acceleration? Explain.

5. An object is moving in a circle and experiences centripetal acceleration. Sometime later, the acceleration is doubled while the velocity remains the same, what must happen to the radius? Explain.

6. An object is moving in a circle and experiences centripetal force. If mass, velocity and radius are all doubled, what happens to the force? Explain.

7. An object is moving in a circle and experiences centripetal acceleration. If mass is doubled while velocity and radius remain the same, what happens to the acceleration? Explain.

8. An object is moving in a circle and experiences centripetal acceleration. Sometime later, the velocity is tripled while the radius is reduced by a factor of 2. What happens to the acceleration? Explain.

9. A 500-kg roller coaster car is at the bottom of a loop on Flight Deck (previously Top Gun). The radius of the loop is 20 m and the speed is 24 m/s.

a. Draw the FBD (with correct sizing and labels) for the box.

b. Determine the following quantities. You must either show your work by identifying the equation used or provide a written response to justify your answer.

m: a: ∑F:

c. Determine the magnitude (size) of each of your forces labeled in your free body diagram. For each force, you must either show your work by identifying the equation used or provide a written response.

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