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Lecture 16 Friday, October 3

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

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Lecture 16 Friday, October 3

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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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