(3)+Newton's+Laws+of+Motion+and+Uniform+Circular+Motion

PAGE EDITORS: shelby hinds, arielle kushman, franklin morgan, liza carroll

Uniform – subject travels in circle at constant speed
 * UNIFORM CIRCULAR MOTION (part 1) **







v = d/ t = 2πr/T = circumference of circle/period __Period (T):__ time it takes to complete one full cycle or circle

1 revolution = 1 circumference = 2πr

*only analyzing reference frames that move at constant velocities with respect to each other **  à called inertial reference frames because Newton’s Laws hold true in those reference frames
 * RELATIVE MOTION IN 1D-3D

__General Approach for Problems:__



FORCES
__Force:__ 1) A vector quantity 2)  A push or pull on an object based on the object’s interaction with another object. (When the interaction ceases, the two objects will no longer experience a force.) 3) Something capable of changing an object’s state of motion, that is, changing its velocity.
 * __Definitions__**

Force is a vector quantity (magnitude and direction).

__** Newton's Laws of Motion **__ __Newton’s 1st Law__ If no net “external” (from environment onto system) force acts on a body/object/system (a.k.a. if Fnet = 0), the system’s velocity cannot change, that is, the system cannot accelerate. no net force: 1) no change in magnitude of the velocity (speed) 2) no change in direction of the velocity The first law is a statement of //inertia//, which is the natural tendency for an object/system to resist a change in its motion. Mass is a quantitative measure of inertia.

__Newton’s 2nd Law__ When an external net force acts on an object of mass “m,” the acceleration “a” is directly proportional to the net force. ΣF= ma Units: mass x acceleration = kg x (m/s2) = the Newton (N) The acceleration will be in the same direction as the net force.

__Newton’s 3rd Law__

** __Friction__ **
 * 1) Weight (W or F g )
 * 2) Tension (T or F T)
 * 3) Normal Force (n or F N)
 * 4) Friction ( f )

Static: -not moving/impending motion

not moving: **f****s****= F(applied)**

object just about to move: **f****s** **= µ** **s x** **F(normal)

Kinetic: -moving relative to other surface in contact **


 * f** **k** **= µk** **x** **F(normal)**


 * µ** **s** greater than **µk** because harder to get something moving than to keep it moving

Coefficient of friction is normally greater than 0 but less than 1




**FREE BODY DIAGRAMS

ex) Mass hangs from two strings ex) mass on two strings positioned to the right ex) system = hanger, rubber band, mass ex) Eraser pressed against wall ex) Eraser pressed against frictionless wall ex) Push against chair, doesn't move ex) Pull chair along floor ex) Book on plane NOT moving ex) Book on plane sliding **

**MORE COMPLICATED**  **FREE BODY DIAGRAMS

ex) Calculator on top of book, pushed at constant speed on table

a) System = book b) System = calculator c) System = calculator during phase of INITIAL acceleration d) System = book during INITIAL acceleration e) System = book + calculator during initial acceleration phase** ** INTERNAL STATIC FRICTION CANCELS OUT! **


 * Solving Force Problems Identifying Forces**
 * 1) Identify system and environment System = object whose motion and interactions you want to study Environment = everything else
 * 2) ** Draw Picture of Situation **
 * 3) Draw FBD
 * General Steps for Solving Force Problem**
 * 1) Draw Picture of Situation
 * 2) Draw FBD
 * 3) Break Angled forces into components
 * 4) Apply component form of Newton's 2nd Law
 * 5) Use Kinematic equations if necessary

[[image:Picture_2.png width="362" height="469"]][[image:Picture_3.png width="359" height="472"]]
click here for word document :

[|Apparent Weight]

**Variable Force Problems - If the force is a function of t (F(t)), you CANNOT use kinematics.**


 * An astronaut in a zero gravity environment throws a hammer of mass "m" through the air. The hammer experiences a resistive force f = bv where b is a constant determined by the size and shape of the object:**
 * a) What are the units of b?**
 * b) Find v(t):**
 * c) Sketch a graph of v vs. t:**
 * d) Find x(t):**
 * e) Taylor expand x(t) for small t (just the first few terms):**

Uniform Circular Motion (part 2: Force Problems)
- For an object moving in a circle, even at a constant speed, there __is__ an acceleration, and therefore there __must__ be a net force. - These problems are solved by applying Newton's 2nd Law of Motion. - Always make your positive direction towards the center of the circle

- What force in your free body diagram is causing the object/ system to move in centripetal motion? 1) Rounding a Flat Curve in Your Car (friction is static because you are not skidding)
 * Basic Diagram and Formulas:**
 * Examples:**

2) Dice in Mirror of a Car in Uniform Circular Motion:



- A component of T (tension) keeps the dice in circular motion.

3) A Plane Turns in the Air:

4) Gravitron: - Inertia pushes the person against the wall.

5) A Rock on a String Swinging in a Vertical Circle: 6) Car Going Around a Banked Curve (assume a frictionless surface):

7) Artificial Gravity: - If the space station rotates at just the right speed, it will mimic gravitational conditions on earth

== http://video.google.com/videosearch?client=safari&rls=en&q=vomit+comet&oe=UTF-8&um=1&ie=UTF-8&ei=9DbmSri5Lt7k8Ab5pZiIBw&sa=X&oi=video_result_group&ct=title&resnum=4&ved=0CCQQqwQwAw#q=Aboard+NASA's+'Vomit+Comet'&view=2&emb=0&client=safari ( //Aboard NASA's// '//Vomit Comet//' - RIT students experience zero gravity while conducting reduced-gravity scientific experiments //**aboard NASA's**// "//**Vomit Comet**//" aircraft; reported by Kelly Downs of RIT University News.) [] (An accurate, not-so-useful comic discussing the centripetal vs. centrifugal force)
 * __Interesting Links, Pictures and Videos__**

=
[] (An article about the 5 points of Lagrange, where gravitation forces balance so something placed at one of these points will remain there - useful for potentially building a space=====  station?)   A diagram showing the five Lagrangian points in a two-body system with one body far more massive than the other (e.g. the Earth and the Moon). In such a system [|L] [|3] –[|L] [|5] will appear to share the secondary's orbit, although in fact they are situated slightly outside it. An object placed in orbit around [|L5] (or [|L4]) will remain there indefinitely without having to expend fuel to keep its position, whereas an object placed at [|L1], [|L2] or [|L3] (all points of unstable equilibrium) may have to expend fuel if it drifts off the point. http://science.howstuffworks.com/space-station.htm/printable (How Stuff Works article about space stations)==

The following report grew out of a 10 week program in engineering systems design held at Stanford University and the Ames Research Center of the National Aeronautics and Space Administration during the summer of 1975. This group worked for ten weeks to construct a convincing picture of how people might permanently sustain life in space on a large scale. [|http://settlement.arc.nasa.gov/75SummerStudy/Table_of_Contents1.html]


 * __SOURCES__**