PH 201

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 x-axis q • Direction angle changes at a constant rate • w is the (constant) “angular velocity” • positive if CCW • So x and y change sinusoidally

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 = 1.5X1011 m • T = 1yr = 3.156X107s = 30,000 m/s = 0.0059 m/s2 huge circle –

9. Newton’s 1st 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 – 1st Law • Recall: 1st 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: S means sum • Note: • there may be several forces; add them. • there is only one acceleration.

14. Centripetal Force – 2nd Law • Recall: centripetal acceleration • An object moving in a circle • is accelerating • Recall: 2nd 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 3rd 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 3rd 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. 3rd 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 onME, • 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)