1. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 1 Lecture 11 Slide 1 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force

2. Introduction Section 0 Lecture 1 Slide 2 Lecture 11 Slide 2 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet *Homework Handout

3. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 3 Lecture 11 Slide 3 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Physics of Technology PHYS 1800 Lecture 11 Circular Motion and Gravitational Force Introduction and Review

4. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 4 Lecture 11 Slide 4 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Describing Motion and Interactions Position—where you are in space (L or meter) Velocity—how fast position is changing with time (LT -1 or m/s) Acceleration—how fast velocity is changing with time (LT -2 or m/s 2 ) Force— what is required to change to motion of a body (MLT -2 or kg- m/s 2 ) We will focus on a special kind of force, termed a central forces [e.g., gravity, Coulombic (charge) or centripetal forces]. Important: Velocity, acceleration and force are VECTORS!!!

5. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 5 Lecture 11 Slide 5 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The Math Approach We are going to explore a different kind of force that is no longer constant, but is proportional to 1/r.  k/r

6. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 6 Lecture 11 Slide 6 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Newton’s Laws in Review 1 st Law —a special case of the 2 nd Law for statics, with a=0 or F net =0 An objects velocity remains unchanged, unless a force acts on the object. 2 nd Law (and 1 st Law)—How motion of a object is effected by a force. –The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force. 3 rd Law —Forces come from interactions with other objects. For every action (force), there is an equal but opposite reaction (force).

7. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 7 Lecture 11 Slide 7 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009  It is the total force or net force that determines an object’s acceleration.  If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions. Net Forces

8. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 8 Lecture 11 Slide 8 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Free Body Diagrams Fancy Science: Vector analysis of complex force problems is facilitated by use of a free body diagram. Common Sense: A picture is worth a 100 words. (A scale picture is worth an A!) Key is to: Isolate a single body and draw all the forces acting on it. Add up all the arrows (vectors). What’s left is the net force. Net force (and masses)  a. A plus initial conditions  motion!

9. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 9 Lecture 11 Slide 9 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009... have anything in common with circular motion on Earth? Does the circular motion of the moon around the Earth...

10. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 10 Lecture 11 Slide 10 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 A ball is whirled on the end of a string with constant speed when the string breaks. Which path will the ball take? a)Path 1 b)Path 2 c)Path 3 d)Path 4 Path 3, in the direction of the tangent to point A. Neglecting gravity, the body would move in the direction it was moving when the force disappeared, in accordance with the first law.

11. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 11 Lecture 11 Slide 11 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 If the string breaks, the ball flies off in a straight-line path in the direction it was traveling at the instant the string broke. If the string is no longer applying a force to the ball, Newton’s First Law tells us that the ball will continue to move in a straight line. Circular motion is called centripetal motion, with the string providing a centripetal force.

12. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 12 Lecture 11 Slide 12 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Centripetal Acceleration Centripetal acceleration is the rate of change in velocity of an object that is associated with the change in direction of the velocity. –Centripetal acceleration is always perpendicular to the velocity. –Centripetal acceleration always points toward the center of the curve (It’s a central force!). F~1/r A central force!

13. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 13 Lecture 11 Slide 13 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Centripetal Acceleration Centripetal acceleration is the rate of change in velocity of an object that is associated with the change in direction of the velocity. –Centripetal acceleration is always perpendicular to the velocity. –Centripetal acceleration always points toward the center of the curve. The centripetal force refers to any force or combination of forces that produces a centripetal acceleration.

14. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 14 Lecture 11 Slide 14 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The horizontal component of T produces the centripetal acceleration. The vertical component of T is equal to the weight of the ball. At higher speeds, the string is closer to horizontal because a large horizontal component of T is needed to provide the required centripetal force. A Simple Demonstration of Centripetal Force (with commentary by Newton)

15. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 15 Lecture 11 Slide 15 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 Centripetal Forces—Negotiating a Flat Curve The centripetal force is the total force that produces a centripetal acceleration. –The centripetal force may be due to one or more individual forces, such as a normal force and/or a force due to friction. The Static force of friction is the frictional force acting when there is no motion along the surfaces. –No skidding or sliding The Kinetic force of friction is the frictional force acting when there is motion along the surfaces.

16. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 16 Lecture 11 Slide 16 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 The friction between the tires and road produces the centripetal acceleration on a level curve. On a banked curve, the horizontal component of the normal force also contributes to the centripetal acceleration. Centripetal Forces—Leaning Into a Curve

17. Circular Motion and Gravitational Force Introduction Section 0 Lecture 1 Slide 17 Lecture 11 Slide 17 INTRODUCTION TO Modern Physics PHYX 2710 Fall 2004 Physics of Technology—PHYS 1800 Spring 2009 What forces are involved in riding a Ferris wheel? Depending on the position: Weight of the rider Normal force from seat Gravity