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Understanding Circular Motion: Acceleration, Forces, and Orbits

Explore the dynamics of circular motion, including acceleration, forces, and orbits. Solve problems and learn about Newton's laws and gravity. Special assignment included. Sample question on vertical loop motion.

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Understanding Circular Motion: Acceleration, Forces, and Orbits

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  1. Lecture 16Friday, October 3 Chapter 6: Circular Motion

  2. Review Example Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-17

  3. For uniform circular motion, the acceleration • Is parallel to the velocity • Is directed towards the center of the circle • is larger for a larger orbit at the same speed

  4. Problem, interacting bodies Glider on a air track Massless, frictionless pulley m1 m2

  5. Special Assignment • Special assignment to be handed in Monday: Workbook pages 4-5 and 4-6, exercises 17-22 and page 5-5, exercises 13-15.

  6. Chapter 6 Circular Motion, Orbits and Gravity Topics: • The kinematics of uniform circular motion • The dynamics of uniform circular motion • Circular orbits of satellites • Newton’s law of gravity Sample question: The motorcyclist in the “Globe of Death” rides in a vertical loop upside down over the top of a spherical cage. There is a minimum speed at which he can ride this loop. How slow can he go? Slide 6-1

  7. Uniform Circular Motion • Uniform magnitude of velocity (speed) is constant

  8. Circular Motion • Note similarity to the equations for one-dimensional linear motion

  9. Going from angular velocity to angular displacement:

  10. UCM continued • Travelling at constant speed v around circle • Period is time one around circle = T

  11. UCM cont • s is distance travelled around circumference and the definition of the radian tell us

  12. Uniform Circular Motion • Uniform magnitude of velocity (speed) ω, is constant • But α is not zero because direction of velocity is changing.

  13. Uniform Circular Motion Slide 6-13

  14. Newton’s Second Law • Net force must point towards center of circle

  15. Example A level curve on a country road has a radius of 150 m. What is the maximum speed at which this curve can be safely negotiated on a rainy day when the coefficient of friction between the tires on a car and the road is 0.40? Slide 6-24

  16. Top View • v

  17. Checking Understanding When a ball on the end of a string is swung in a vertical circle: • What is the direction of the acceleration of the ball? • Tangent to the circle, in the direction of the ball’s motion • Toward the center of the circle Slide 6-11

  18. Problems due today • 5: 24, 25, 29, 30, 31, 35, 36, 37, 39

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