1. Circular Motion

2. The situation below is called uniform circular motion. 20ms -1

3. WHY is this called uniform circular motion? Because the car is travelling in a circle at a Constant Speed 20ms -1

4. Is a car accelerating when it is undertaking uniform circular motion? 20ms -1 Because: The velocity is changing. The speed may be constant but the direction is continually changing and so the car is continually accelerating as it moves around the circle. YES?

5. What are two important characteristics about the acceleration on the car below? The acceleration: is always towards the centre of the circle constant in magnitude 20ms -1 a a a a a a a a

6. Why must the acceleration be towards the centre of the circle in uniform circular motion? When the acceleration is towards the centre of the circle it is perpendicular to the motion. Being perpendicular to the motion there is no component of the acceleration along the direction of motion so the there is no increase in the speed, BUT THERE IS A CHANGE IN DIRECTION. 20ms -1 a a a a a a a a

7. Why must the acceleration be constant in uniform circular motion? Because the acceleration is only changing the direction of the velocity and the direction is constantly changing by the same amount to form a circle, the acceleration must be constant. 20ms -1 a a a a a a a a

8. Is there a net force on an object undergoing uniform circular motion? Since the car is accelerating towards the centre of the circle there must be net force towards the centre of the circle. 20ms -1 F net 20ms -1 a a a a a a a a

9. How can we work out the magnitude of the acceleration? 20ms -1 a a a a a a a a

10. How can we work out the magnitude of the net force? 20ms -1 F net

11. Possible Questions

12. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (a) On the diagram below draw an arrow showing the net force on the car at X. F net

13. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (b) On the diagram below draw arrows to show all the separate forces acting on the car at point X, ignoring air resistance. The arrows must show both the direction of the forces represented and the point of application of each force W N Fr

14. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (c) Draw an arrow below showing the force of the car on the road at X. F car on road F net

15. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (d) At Y the car starts slowing down, draw an arrow showing the net force on the car. F tan F cent F net

16. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (e) Draw an arrow showing the net force at Y if the car was actually speeding up. F tan F cent F net

17. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (f) Draw an arrow showing the force of the car on the road in question e). F tan F cent F net F car on road

18. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (g) What is the net force on the 1000kg car at X? F net

19. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (h) What is the acceleration on the car at X? F net

20. Question 1 The 1000kg car below is travelling around the curve at a constant speed of 10.0ms -1. (i) If the maximum safe speed for the car on this curve is 20ms -1, what is the minimum safe curve radius for the car on this sort of surface if it was travelling at 40ms -1 ? This question will be dealt with next Physics lesson

21. Question 2 (a) The diagram opposite shows a car that has been able to safely travel around a corner in icy conditions where there is negligible friction. Draw in the forces on the car. This question will be dealt with next Physics lesson

22. Question 2 (b) Explain why banking will allow the car to be able to safely negotiate the curve without skidding off the road? This question will be dealt with next Physics lesson

23. Question 2 (c) What is the normal reaction of the road on the car if bank is 10 o to the horizontal, the curve has a radius of 100m and the car is travelling at 25ms -1 ? This question will be dealt with next Physics lesson

24. Question 3 Derive the formula for working out the banking angle would be required for a car to go around a curve of radius r at a speed of v? This question will be dealt with next Physics lesson

25. Question 4 What speed limit should be put on the 80m banked curve opposite if the road is subject to ice? This question will be dealt with next Physics lesson

26. Question 5 In the sketch below Jim is sitting in a carriage frictionlessly moving through a valley in a roller coaster ride. Jim has a mass of m kg, and the valley is close to circular, with a radius of r m. The carriage he is sitting in is travelling at v ms -1. The gravitational field is represented by g. (a) Draw in the forces acting on Jim with appropriate relative sizes W N Give a qualitative reason to explain why must N be greater than W Because Jim is undergoing uniform circular motion the net force has to be the towards the circle so N has to be greater than W.

27. Question 5 In the sketch below Jim is sitting in a carriage frictionlessly moving through a valley in a roller coaster ride. Jim has a mass of m kg, and the valley is close to circular, with a radius of r m. The carriage he is sitting in is travelling at v ms -1. The gravitational field is represented by g. (b) Why does Jim feel heavier? W N +

28. Question 5 (c) If Jim’s mass is 65kg, r = 20m and v = 10ms -1 what is the magnitude of the acceleration of Jim at the bottom?

29. Question 5 (d) If Jim’s mass is 65kg, r = 20m and v = 10ms -1 what is the Normal Reaction on Jim?

30. Question 5 (e) If Jim’s mass is 65kg, r = 20m and v = 10ms -1 what is the G Force on Jim?

31. Question 5 (f) If Jim’s mass is 65kg, r = 20m and v = 10ms -1 how much heavier will Jim feel (as a percentage)? % Apparent Weight

32. Question 5 extra If Jim’s mass is 65kg, r = 20m and v = 10ms -1 what mass would register on a set of spring scales? % Apparent Mass

33. Question 5 (g) A short time later Jim is travelling over a hill on the roller- coaster. He now feels lighter than usual. Explain why Jim feels lighter than usual. Include a force diagram in your explanation? N W +

34. Question 5 (h) If the hill had a radius of 12m, what is the maximum speed that the cart can travel at without leaving the track?

35. Question 5 (i) How much lighter will Jim feel if the cart is travelling at 3.0 ms -1 remembering that he is 65kg in weight and the curvature of the hill is 12m in radius? ???

36. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (a) Calculate the speed of the car at C (Ignore friction and air resistance? 22m v = ? m = 250kg h = 22m g = 10Nkg -1 U g  E k mgh = ½ mv 2 gh = ½ v 2 10 × 22 = ½ × v 2 220 = ½ × v 2 440 = v 2 20.9762 = v 2 v  21 ms -1 8.0m

37. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (b) What will be the normal reaction on the cart at C? 22m 8.0m

38. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (c) What is the minimum speed required for the cart to stay in contact with the track at point D if it is not securely attached to the track? 22m 8.0m

39. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (d) What speed will the car be going at D (if the car stays on the track)? 22m 8.0m v = ? m = 250kg u = 20.9762 ms -1 h = 16m g = 10Nkg -1 E k i  E k f + U g ½ mu 2 = ½ mv 2 + mgh ½ u 2 = ½ v 2 + gh u 2 = v 2 + 2gh 20.9762 2 = v 2 + 2 × 10 × 16 440 = v 2 + 320 120 = v 2 10.954452 = v v  11 ms -1

40. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (d) What speed will the car be going at D (if the car stays on the track)? 22m 8.0m v = ? m = 250kg h = 6m g = 10Nkg -1 U g  E k mgh = ½ mv 2 gh = ½ v 2 10 × 6 = ½ × v 2 60 = ½ × v 2 120 = v 2 10.954452 = v v  11 ms -1 8.0m 6.0m OR This may not be your first choice to solve this problem but it is the only practical way of finding the speed after a series of up and downs on a roller coaster, because you can ignore the ups and downs and just look at the start and end of the path.

41. Question 6 A ride at an amusement park involves passengers ‘looping the loop’, in a car as shown. The car starts from rest at A, which is 22m above C. The car and its passengers have a combined mass of 250kg. The circular part of the tract (with C at the bottom and D at the top) has a radius of 8m. (e) What will be the normal reaction on the cart at D ? 22m 8.0m

42. Question 7 A circular humpback bridge is shown below. A sign before the bridge advises: ‘Cars may lose contact with the road surface at the crest if they exceed a speed of 36kmh -1 (=10ms -1 ). (a) The bridge radius (at its crest) is 10m. What is the acceleration of the truck if it is travelling at 10ms -1 at the crest. This question will be dealt with next Physics lesson

43. Question 7 A circular humpback bridge is shown below. A sign before the bridge advises: ‘Cars may lose contact with the road surface at the crest if they exceed a speed of 36kmh -1 (=10ms -1 ). (b) Explain why the truck is likely to lose contact with the road surface at this speed. This question will be dealt with next Physics lesson

44. Remainder of The Circular Motion Notes The solution to the rest of the circular motion notes and examples are still being created.