1. Momentum

2. Momentum Momentum = mass x velocity
Momentum is a measure of how hard it is to stop something.
Momentum = mass x velocity
Which has most momentum? v v

3. Which has most momentum?v 2v

4. Momentum Conservation
The total momentum of a system is constant unless there is an external ….
FORCE
Δp = if F = 0

5. Momentum is a vector quantity

6. Total initial momentum = mv + (-mv) = 0 Total final momentum = 0

7. Kinetic energy is a scalar.
Bull’s Total Initial KE =
Bull’s Total Final KE = 0
Kinetic energy is converted to heat

9. Total initial momentum = 0
Total final momentum = Mv + (-mV)
= 0

11. Impulse
Describe how you catch an egg to minimise the chance of it breaking.
The damage to the egg (force on it) doesn’t just depend on how fast it’s travelling….
but also how fast it stops.

13. The momentum change for the egg does not depend on how you catch it ( )
A long stopping time causes a small force or

14. Summary of Key Ideas
Momentum is always conserved if there are no outside forces.
(the momentum of a sliding box decreases because friction is an outside force)
Kinetic Energy is not usually conserved in most interactions KE is converted to HEAT

15. Centre of Mass Centre of mass
This is the point where you can assume all the weight force acts through.
Centre of mass

16. The centre of mass is normally above the support
Where is the center of mass?

17. Will He Balance?

18. Where is her centre of mass?

19. mc x dc= mAC x dAC clockwise torque = anticlockwise torque
(mc g) x dc= (mAC g) x dAC
mc x dc= mAC x dAC

20. Center of Mass Where is the center of mass? 3 x d = 2 x (2 – d)
3 kg
2 kg
2 m d
2 - d
Where is the center of mass?
3 x d = 2 x (2 – d)
d = 4/5 =0.8 m

21. Center of Mass x - d d Where is the center of mass?
m1 x d = m2 x (x – d)

22. If momentum is conserved, the centre of mass has constant velocity

23. Collisions in Two Dimensions
Inelastic Collision

25. Collisions in Two Dimensions Inelastic Collision

27. Adding Momentum Vectors
Total final momentum
BEFORE
pB after
pA = 3 kgms-1
pA before
pB = 3 kgms-1

28. Collisions in Two Dimensions Elastic Collision

31. Vector Triangle Method

32. Total final momentum
pB after
Same as initial momentum
pA = 3 kgms-1
Σp = 3 kgms-1
pA after

33. Total final momentum
Same as initial momentum
pA = 3 kgms-1
pB after
pA after

34. pi = 6 kgms-1 Σp = 6 kgms-1 pX = 3 pf = 5 kgms-1 pY = 4 370 370 pY = 4

35. Components Method

36. What is the momentum of the red ball after the collision?
pX = 6
pA = 10 kgms-1
pY = 8
pi = 12 kgms-1
Σp = 12 kgms-1
370
What is the momentum of the red ball after the collision?
pY = 8
P B= 10 kgms-1
pX = 6

37. Momentum Change Find the momentum change of the ball Recall Δp = pf-pi
or Δp = pf + (-pi) pf Δp pi
Check momentum change of the ball is in the same direction as the force

38. Momentum Change Δp Find the momentum change of the ball
Recall Δp = pf-pi
or Δp = pf + (-pi) pf
-pi pi pf Δp
Check momentum change of the ball is in the same direction as the force

39. Force of racket on ball
Force of ball on racket

40. Find the momentum change of the 300g soccer ball.
Find the average force on the ball if she was in contact for 0.10s
15 ms-1
20 ms-1

41. Circular Motion

42. A car goes around a circle as shown. What direction is the net force?B A C D

43. The car hits an icy patch as shown. What direction will it slide?B C

44. Objects moving in a circle are always accelerating towards the centre.
Centripetal acceleration is….
This requires a centripetal force.

45. We will look at circular motion with two forces

46. Don’t watch this if you’re a cat lover……..

48. A bird swings in a horizontal circle on a string.
What are the individual forces?
What is the total force?
What direction is the acceleration?
What happens as it speeds up?

50. Why do motorcyclists lean when cornering?

51. Consider the forces
Straight line

52. Consider the forces
Cornering upright
Centripetal force
Which way is he turning?
What will happen? (consider Torque about center of mass)

53. Consider the forces
Cornering leaning
Centripetal force
What will happen? (consider Torque about center of mass)
clockwise torque = anticlockwise torque

55. Vertical Circular Motion

56. Why doesn’t he fall at the highest point?

57. What happens to the penguin if the lift is stationary? Why?
acceleration = 0
Gravity pulls the penguin down, the elevator produces an equal and opposite force up

58. What happens to the penguin if the lift is accelerates up at 10ms-2?
Why?
acceleration
Gravity pulls it down, the elevator produces a force up that is twice its weight.

59. What happens to the penguin if the lift is accelerates down at 10ms-2?
Why?
acceleration
The penguin is in freefall. There is no upward force on the penguin from the elevator.
When we feel “weight”, it is the upward force from the floor. The penguin thinks she is weightless

60. What happens to the penguin if the lift is accelerates down at 15ms-2?
Why?
acceleration
The penguin is stuck to the ceiling of the elevator.
She is accelerating at more than 10 ms-2, so an extra force is needed. (this is from the elevator floor)

61. Roller Coaster
Why does the car not fall?
It is falling!! But it’s also moving sideways.
If the centripetal acceleration is greater than 10 ms-2 the car will stay on the track
This is like being in an elevator accelerating down at › 10ms-2. You will be on the ceiling.

62. Gravity and Satellites
How are you able to watch the All Blacks on TV when they are playing in France?
How are you able to have a cellphone conversation with your friend in the USA?

64. International Space Station

67. Other Uses of Satellites
Tracking endangered animals

68. Satellite Weather Forecasting

69. Satellites
Satellites are above the atmosphere (no air resistance), so the only force on them is…………. Gravity

70. Why don’t satellites fall?
link to Newton's mountain
Satellites are falling, but they are moving sideways,
They fall at the same rate that the earth curves away under them

72. Weightlessness.
You don’t feel the gravity force on your body, you feel the support force pushing up.
You can feel weightless for two reasons.
1: You are weightless in outer space. There is no gravity force so there is no reaction force

73. You feel weightless in orbit
You feel “weight” due to the support force on you.
The astronaut and their satellite are in free fall.
There is no support force acting on them

74. Newton’s Law of Gravitation

75. Can a satellite have any speed?
At a certain height, a satellite must have one particular speed.
Satellite Speed:

76. Period of a satellite
The period of a satellite orbiting around the earth only depends on the altitude.

78. Notice the mass of the satellite doesn’t appear in the equation.
All masses have the same acceleration due to gravity:

80. A geostationary satellite has a period of 24 hours
It must have the earth’s centre as its orbital centre
It must be above the equator

81. Geostationary Satellites
AUS NZ

82. AUS NZ

83. AUS NZ

84. AUS NZ

85. AUS NZ

86. AUS NZ

87. AUS NZ