1. PH 201 Dr. Cecilia Vogel Lecture

2. REVIEW  Projectiles  Dropping  Upward throw  Range OUTLINE  Newtons Laws  Force, mass, inertia  action, reaction forces

3. Special Case: Uniform Circular Motion   is the (constant) “angular velocity”  positive if CCW  So x and y change sinusoidally  Direction angle changes at a constant rate x-axis 

4. Period of Motion  Period, T, is the time it takes  time to go  If it goes all the way around once, the angle changes by (rad)  If it goes all the way around once, the distance traveled is

5. Special Case: Uniform Circular Motion  An object moves in a circle of constant radius, r, with constant speed, v.  Is the object accelerating?   Consider ways of ID’ing acceleration:  physical intuition: force needed, jerk felt  math:

6. Acceleration  What is the acceleration of the object at  Consider the average acceleration from just before to just after:  Generally: centripetal acceleration is

7. Magnitude of Acceleration  Same r and larger v yields:   Same v and smaller r yields:   Same T and larger r yields:  

8. Example  What is the speed and acceleration of the Earth in orbit?  r = 93,000,000 mi = 1.5X10 11 m  T = 1yr = 3.156X10 7 s = 30,000 m/s = 0.0059 m/s 2 huge circle –

9. Newton’s 1 st Law An object at rest remains at rest, object in motion remains in uniform motion (i.e. constant velocity, no change in speed nor direction) unless acted on by a net external force. demos

10. Inertia Inertia is the word used to describe this tendency: It is NOT a resistance to motion It is a resistance to CHANGE in motion Inertia is a property of matter. Define mass: if an object has inertia, then it has mass.

11. Centripetal Force – 1 st Law  Recall: 1 st Law  An object in motion will continue   no change Can only continue in circle if

12. Newton’s Second Law  An net external force can change an object's velocity, can accelerate it.  The force required is proportional to the acceleration, and in the same direction.  The force required is also proportional to the object’s mass.

13. Newton’s Second Law Improved  What is meant by “net” external force?  take all the external forces, and add them as vectors.  the resultant is the net force.  Notation:  means sum  Note:  there may be several forces; add them.  there is only one acceleration.

14. Centripetal Force – 2 nd Law  Recall: centripetal acceleration  An object moving in a circle  is accelerating  Recall: 2 nd Law  in order for object to accelerate   The acceleration is toward center, so  centripetal force is

15. Centripetal Force – Examples  What force holds each in circular motion?  A ball swung around on a string:   You, as you rotate around with Earth’s surface:   Amusement-park ride: you’re plastered to the wall and the floor drops out   Coin on a turntable 

16. Newton’s Third Law  “For every action, there is an equal and opposite reaction”  Better said: “For every FORCE, there is an equal and opposite reaction FORCE.”  If A pushes on B,  then B pushes back on A  at the same time.

17. Newton’s 3 rd Law  For every FORCE, there is an equal and opposite reaction FORCE.  If I try to push the door open, the door pushes back on me,  making it hard to open a door in a wheelchair.  If the Earth pulls down on me with a gravitational force, then I pull up on the Earth  with exactly the same size force!

18. More on the 3 rd Law  The object pushes back, even if it accelerates.  when you shoot a gun  you accelerate bullet forward  you can feel it push _________ on you  “recoil”  when you catch a ball  you accelerate it backward (to stop it)  you can feel it push __________ on you

19. 3 rd Law Reaction on What?  The “action” FORCE and the “reaction” FORCE don’t act ON the same thing.  If the action force is Earth’s gravity pulling on ME,  then the reaction force is me pulling on the Earth.  If the action force is your behind pushing down on the chair,  then the reaction force is the chair pushing up on your behind (keeping you from falling)