1. Chapter 3 Nonlinear Motion

2. 1.MOTION IS RELATIVE Example: Motion of a boat with respect to the ground and with respect to the river. Velocity of river Velocity of boat with respect to river Velocity of boat with respect to ground Add the velocity of the river

3. Velocity of river Velocity of boat with respect to river Velocity of boat with respect to ground Add the velocity of the river

4. Velocity of river Velocity of boat with respect to river Velocity of boat with respect to ground

5. 2.VELOCITY - A VECTOR QUANTITY l Scalars are quantities that are specified by magnitude only. l Examples: distance, time, mass, density l Vectors are quantities that are specified by magnitude and direction. l Examples: displacement, velocity, acceleration, force, momentum, angular momentum

6. 4 miles east 3 miles north 5 miles 37 0 north of east The Displacement Vector What is the displacement for this trip?

7. 3.PROJECTILE MOTION l Projectile motion is a combination of vertical free-fall motion and horizontal motion at a constant speed.

8. Parabola (approximately)

9. l Demo - Ball projector and dropper l Demo - Monkey in tree l Demo - Cart and ball launcher l Demo - Wall parabola

10. The free-fall motion of a projectile near the surface of the earth is very nearly parabolic. A parabola is one of the of a conic sections. Circle EllipseParabolaHyperbola

11. For a particular range less than the maximum and for a particular launch velocity, two different launch angles will give that range. The two angles add to give 90 0. 45 0 gives the maximum range. Simulation

12. Free Fall Results l Horizontal motion is constant l Vertical Motion is accelerated l Rise time = Fall Time l Final speed = Initial speed

13. l Actual path and ideal path (free fall) are different.

14. 4.FAST-MOVING PROJECTILES - SATELLITES l Lets throw stones horizontally with ever increasing velocity. l The Earth’s curvature is 16 ft for every 5 miles (4.9 m for 8 km).

15. 16 ft Curvature of Earth 5 miles Throw an objectfaster,faster.faster, We draw in each trajectory for 1 second

16. Ellipse Ellipse - Circle Ellipse Parabola V circle = 5 mi/s = 8 km/s V escape = 7 mi/s = 11 km/s Hyperbola

17. 4.CIRCULAR MOTION Linear speed and rotational speed c Linear speed is a distance divided by time. c Rotational speed is an angle measurement divided by time.

18. AB Which fly has the greater linear speed? B Which fly has the greater rotational speed? Same for both. AB AB AB AB AB Two Flies on a Turntable

19. Chapter 3 Review Questions

20. A rock is thrown upward at an angle. What happens to the horizontal component of its velocity as it rises? (Neglect air resistance.) (a) it decreases (b) it increases (c) it remains the same

21. In the game of baseball which path would a home run most closely approximate? (Neglect air resistance.) (a) hyperbolic (b) parabolic (c) eccentric (b) parabolic

22. A projectile is launched upward at an angle of 75 o from the horizontal and strikes the ground a certain distance down range. What other angle of launch at the same launch speed would produce the same distance? (Neglect air resistance.) (a) 45 0 (b) 15 0 (c) 25 0 (b) 15 0

23. A horizontally traveling car drives off of a cliff next to the ocean. At the same time that the car leaves the cliff a bystander drops his camera. Which hits the ocean first? (Neglect air resistance.) (a) car (b) camera (c) they both hit at the same time

24. Bug A is 3 inches from the center of a rotating 33.33 rpm record. Bug B is 5 inches from the center of the same record. Bug A has linear speed and rotational speed as bug B. (a) less, less (b) less, same (c) same, less (d) same, same (e) less, greater (b) less, same