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Circular Motion

Circular Motion. Introduction. What is Newton’s First Law how does it relate to circular motion? How does Newton’s second law relate to circular motion? . Acceleration. V i. V i. V f. V f. V i. V f. V f. Acceleration. In uniform circular motion, which direction is the acceleration?

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Circular Motion

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  1. Circular Motion

  2. Introduction • What is Newton’s First Law how does it relate to circular motion? • How does Newton’s second law relate to circular motion?

  3. Acceleration Vi Vi Vf Vf

  4. Vi Vf Vf

  5. Acceleration • In uniform circular motion, which direction is the acceleration? • There is no component of the net force adding to the speed of the particle. • Therefore, the net force must always be perpendicular to the Velocity Vector. • The acceleration of a particle in uniform circular motion is always towards the centre of the circle. • The particle is always deviating from it’s straight line path towards the centre of the circle.

  6. Exam Question (VCAA 2010) A racing car of mass 700 kg (including the driver) is travelling around a corner at a constant speed. The car’s path forms part of a circle of radius 50 m, and the track is horizontal. The magnitude of the central force provided by friction between the tyres and the ground is 11 200 N. Question 1 What is the speed of the car? (2 marks) Question 2 What is the acceleration of the car as it goes around the corner? (2 marks)

  7. Exam Question (VCAA , 2009) Question 3 Draw an arrow to show the direction of the net force on the motorcycle.

  8. On the diagram, draw the forces acting on the car. Remember the car is travelling in a circular path. Centre of circular path

  9. On the diagram, draw the forces acting on the car. Remember the car is travelling in a circular path. Centre of circular path FN FN Ff Ff Fg

  10. On the diagram, draw the forces acting on the car. Remember the car is travelling in a circular path. Centre of circular path FN FN Since the vertical forces are balanced, the net force (which we call centripetal force) is the sum of the sideways frictional forces. Ff Ff Fg

  11. Ball on a string

  12. Ball on a string Fg

  13. Ball on a string Ft Fg

  14. Ball on a string Ft Fg Ft Fg

  15. Ball on a string Ft Fg Ft Fg

  16. Ball on a string Ft Fg Ft Fg

  17. Example: Ball on a string A ball of mass 250 g is attached to string in a game of totem tennis. The string makes an angle of 40o to the vertical pole. Calculate: a. the net force on the ball b. the tension in the string c. the length of the string in terms of it’s speed, v?

  18. Banked Corners

  19. Banked Corners Fg

  20. Banked Corners FN Fg

  21. Banked Corners FN Fg Fg FN

  22. Banked Corners FN Fg Fg FN

  23. Banked Corners FN Fg Fg FN

  24. Banked Corners FN Fg Fg FN

  25. Banked Corners FN Fg Fg FN

  26. Exam Question: VCAA 2010 Question 4 On the diagram, draw an arrow to indicate the direction of the acceleration of the rider (1mark)

  27. Exam Question: VCAA 2010 Question 5 The circular path of the bicycle has a constant radius of 120 m, and the bicycle will be travelling at a constant 9 m s-1. What should be the value of the angle of the bank, θ, so that the bicycle travels around the corner with no sideways frictional force between the tyres and the track? (3 marks)

  28. Banked Corners FN Fg The force diagram doesn’t consider friction. Challenge: What would the force diagram look like if we considered friction? In which direction would the net force be? Fg FN

  29. Leaning into corners

  30. Leaning into corners FN Ff Fg

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