 Think of a "FIELD" as:
 an invisible influence capable of exerting a force on a MASS or CHARGE
 Universal Law of Gravitation (formula)
F_{g}=Gm_{1}m_{2}/r_{2}
 The Universal Law of Gravitation is true everywhere, but NEAR EARTH'S SURFACE:
 What do we assume?
 What formula can we simplify to?
 What do we assume?
 What formula can we simplify to?
 Assume g= 10 m/s^{2}
 Simplify to:
 F=mg
 Simplify to:
 F=mg
 Give the PE_{grav} formula NEAR EARTH
For FLUIDS (which DON'T always move as a single uni), what change to the formula do we make?
PE_{grav}=mgh
 For fluids:
 use PE_{grav}=pgh
 p=density=m/v
 use PE_{grav}=pgh
 Give the PE_{grav}formula

IN SPACE, or

NEAR EARTH'S SURFACE
 if we AREN'T assuming g=10 m/s^{2}
 IN SPACE, or

NEAR EARTH'S SURFACE
 if we AREN'T assuming g=10 m/s^{2}
PE_{grav}=  Gm_{1}m_{2}/r
Radius is NOT squared here!!!
 Friction opposes ____, not ____
SLIDING!
 not motion
 If theres SLIDING, it's ___ friction
 If NOT, its ___ friction
 sliding= kinetic friction
 not sliding=static friction
 Give the formulas for static & kinetic friction
STATIC FRICTION:

F_{f}=U_{s}Fn
 or F_{f}=U_{s}mgcosθ
KINETIC FRICTION:

Ff=U_{k}Fn
 or F_{f}=U_{k}mgcosθ
U_{s} / U_{k} = Coefficient of static/kinetic friction
F_{s} / F_{k}= Force of static/kinetic friction
n= "normal force"=mgcosθ
 Define MAX static friction
 once this value is reached, OBJECT BEGINS TO SLIDE
 at this moment, we now have kinetic friction, NOT STATIC
 at this moment, we now have kinetic friction, NOT STATIC
Ex: no mvmt at 500 N (static) but starts moving at 501 N=kinetic
 Inclined Planes
 Give the equation for:
 Force down an inclined plane
 parallel to the surface
 Give the equation for:
 Force down an inclined plane
 parallel to the surface
 Force down an inclined plane
F=mgsinθ
 Inclined planes:

Normal force on an Inclined Plane
 Equation=?

Normal force on an Inclined Plane
 Equation=?
F_{n}=mgcosθ
 Inclined planes:
 Velocity of a particle at the base of an inclined plane
 Equation=?
 Velocity of a particle at the base of an inclined plane
 Equation=?
V_{f}=√2gh
 Inclined planes

ACCELERATION down an inclined plane
 Equation=?
 ACCELERATION down an inclined plane
 Equation=?
a=gsinθ
Hooke's Law formula
F=kΔx
 How do you calculate k (spring constant) by hanging weights?
 Remember calculation is different for just doing ONE trial and doing TWO (+) trials
 Remember calculation is different for just doing ONE trial and doing TWO (+) trials
 Solve using Hooke's Law
 F=kΔx
 for Δx, use:

Displacement from equilibrium point
 for ONE trial

Difference in displacement
 between TWO trials
 For F, use:

Force applied in ONE trial, or

Difference in force
 between TWO trials
 Remember to convert mass of object to force

using F=mg
 F=kΔx
 for Δx, use:

Displacement from equilibrium point
 for ONE trial

Difference in displacement
 between TWO trials

Displacement from equilibrium point
 For F, use:
 Force applied in ONE trial, or

Difference in force
 between TWO trials
 using F=mg
 PE_{elastic }

_{}Definition
 Equation=?
 _{}Definition
 Equation=?
PE_{elastic}=½kΔx^{2}
 PE_{elastic}= PE stored in a compressed spring
 PE_{elastic} most likely used for what kinds of questions?
 How would you use PE_{elastic} to find out how far a spring compresses when an object hits it?
Conservation of energy questions!
 When a mass of velocity V hits a spring:
 ALL of its KE is converted into PE_{elastic}
 Setting KE_{initial} equal to final PE_{elastic}
 ...lets you find how far the spring will compress
 Kinetic Energy equation=?
KE=½mv^{2}
 Finding how far a spring compresses
 What COMBINATION of formulas would you use?
 What COMBINATION of formulas would you use?
Set KE equal to PE_{elastic}
 _{}½mv^{2 }= ½kΔx^{2}

ONE CYCLE of a pendulum is?
 (LOTR)
 (LOTR)
 "There and back again"
 For a pendulum to exhibit Simple Harmonic Motion (SHM)...
 What value must be LOW?
 What value must be LOW?
 Angle of displacement
Give 3 examples of Simple Harmonic Motion
 Pendulum
 mass on a string
 Things w/ circular motion when viewed from the side
 Ex: Something bobbing up & down in the water
 has a circular motion!
 Waves sloshing back & forth in a container
 mass on a string
 Ex: Something bobbing up & down in the water
 has a circular motion!

Simple Harmonic Motion
 Give the Mass on a Spring formula
 Give the Mass on a Spring formula
T=2π√m/k

Simple Harmonic Motion
 Give the pendulum formula
 Give the pendulum formula
T=2π√L/g

Simple Harmonic Motion
 What is "T?"
 What thing is its inverse?
 What is "T?"
 What thing is its inverse?
T=period
 inverse to frequency
 f=1/T
 Objects at rest are in ___ equilibrium
STATIC equilibrium
 Objects moving at CONSTANT velocity are in ___ equilibrium
DYNAMIC equilibrium
 What do you do to solve equilibrium problems?
 Hint: make a T...
 Hint: make a T...
Make a T
 put opposing forces on opposite sides
 balance them out
 Ex: If 180 N in downward direction
 then 180N upward
 Give 3 examples of equilibrium
 Terminal velocity
 mg=F_{air}

Constant velocity
 Objects at rest
 mg=F_{air}

Torque formulas3 variations)
 Break down what each part represents
 Break down what each part represents
 T=fl
 T=mgl

T=Frsinθ
 l=lever arm
 r=dist b/t force & point of rotation
 l=lever arm
 r=dist b/t force & point of rotation
 In Torque equation:

r = l only when...?
 What is always equal to "l?"
 r = l only when...?
 What is always equal to "l?"
r = l only when θ=90°
 "rsinθ" is always equal to l
 To solve for:
 fulcrum and boards on strings problems
 Hint: these are in equilibrium
 fulcrum and boards on strings problems
 Hint: these are in equilibrium
Set:

T_{clockwise}=T_{counterclockwise}
 _{}include ALL torques!
 Torque
 In what scenario would you use T=Frsinθ?
 In what scenario would you use T=Frsinθ?
 When Force applied is NOT perpendicular to the surface
 i.e., when θ is NOT 90°
 i.e., when θ is NOT 90°
 Define:
 systems NOT in equilibrium
 systems NOT in equilibrium
 where the object has NONZERO ACCELERATION
 When solving for systems NOT in equilibrium:
 How do you solve it differently than systems that are in equilibrium?
 What can you IGNORE when solving for systems that are not in equilibrium?
 How do you solve it differently than systems that are in equilibrium?
 What can you IGNORE when solving for systems that are not in equilibrium?
 Solve in same way as equilibrium problems (T method
 but add "ma" to the "losing side"
 This equals it out
 but add "ma" to the "losing side"
 This equals it out
You can IGNORE SIGNS (+/) when you do this method!
 Equilibrium on an Inclined Plane
 How to solve?
 How to solve?
Use T method

One side= UP forces

Other side=DOWN forces
 Down forces always equal to F=mgsinθ
 since force of friction is always parallel to the plane opposite the direction of motion
 Down forces always equal to F=mgsinθ
How to solve problems involving 2D forces
Use T method
 Put formula that predicts component of each force into boxes
 Add "ma" onto the "losing side"
Define the "right hand rule" for angular velocity (ω)
 Curl fingers around axis of rotation, so that fingers are pointing in the direction of rotation
 Your thumb will then be pointing in the direction of the vector (ω)
 Your thumb will then be pointing in the direction of the vector (ω)
How many radians per 1 revolution
~6
 6.28 exactly
How to convert Radians to degrees
 2π radians/360°
or
 π radians/180°
 An object is in rotational equilibrium IF:
 2 options...either one or the other
 2 options...either one or the other
 It is NOT rotating, or
 It is rotating with constant ω (angular velocity)

Momentum formula=?
p=mv
 Think of momentum as?
 When is it always conserved?
 When is it always conserved?
...as INERTIA INCREASED BY VELOCITY
 p is always conserved in an isolated system
 is not conserved when not in an isolated system
 Define "Impulse"

change in an object's momentum
 "Δp"
 "Δp"

Impulse formula
 3 variations (in order of how you should think of impulse)
 3 variations (in order of how you should think of impulse)
 I=Δp
 I=mΔv
 I=F_{avg}t
 What are common impulse questions?
 How are velocity and impulse related?
 How are velocity and impulse related?
CAR CRASHES!
 No change in V= No impulse
 High change in V=High impulse
 Elastic vs Inelastic collisions
Elastic Collisions
 p AND KE conserved
Inelastic Collisions
 p conserved ONLY
 If object is deformed during collision, it was a _____ collision
 inelastic
 Elastic collisions
 Equation=?
 Hint: What gets conserved during elastic collisions?
 Equation=?
 Hint: What gets conserved during elastic collisions?
½m_{1}v_{1}^{2}+ ½m_{2}v_{2}^{2}= ½m_{1}v_{1}^{2}+ ½m_{2}v_{2}^{2}
 p and KE both conserved
 For PERFECTLY elastic collisions, what 2 weird things happen?
 What's a (albeit imperfect, but close enough) example of this?
 What's a (albeit imperfect, but close enough) example of this?

Speed is conserved
 before AND after collision
 If mass of 2 objects is equal but they have different velocities:
 velocities get exchanged
 in order to conserve momentum (p=mv)
 before AND after collision
 velocities get exchanged
 in order to conserve momentum (p=mv)
Think of: BILLIARD BALLS

Inelastic collisions formula
 What thing DO you need to remember to use here that you DON'T need to use for elastic collisions?
 What thing DO you need to remember to use here that you DON'T need to use for elastic collisions?
m_{1}v_{1}+m_{2}v_{2}=m_{1}v_{1}+m_{2}v_{2}
You need to remember to USE SIGNS!! (+/)
 Velocity has a negative sign when:
 going to the LEFT or
 DOWN
 "Perfectly INelastic" collisions
 definition & formula
 definition & formula
 objects collide and stick together
 it's like MARRIAGE!
 if they move after collision, they do so together
 it's like MARRIAGE!
m_{1}v_{1}+m_{2}v_{2}=(m_{1}+m_{2})v_{3}

Reverse Collisions definition
 What is commonly use by the MCAT to test you on reverse collisions?
 What is commonly use by the MCAT to test you on reverse collisions?
 Two objects start out together and come apart
 it's like DIVORCE
 it's like DIVORCE
Common examples:
 Bomb exploding
 Also, RADIOACTIVE DECAY is frequently used

Thermal expansion formula
ΔL=αL_{o}ΔT
 Heating solids leads to ___
 Cooling solids leads to ___
 expansion
 shrinkage
 What makes water unique when it comes to thermal expansion?
 When temperature of water gets close to zero, it EXPANDS (INSTEAD OF SHRINKING)
 because of of highly ordered lattice structure of ice
 This is why the solid ice doesnt sink on liquid water
 because of of highly ordered lattice structure of ice
 This is why the solid ice doesnt sink on liquid water
 PE_{elec}
 formula=?
 2 variations
 formula=?
 2 variations
 PE_{elec}=Kq_{1}q_{2}/r
or
 PE_{elec}=qEd
 PE_{capacitor} formula=?
 3 variations
 3 variations
 PE_{capac}=½QV
 PE_{capacitor}=½CV^{2}
 PE_{capacitor}=½Q^{2}/C

Internal energy
 definition
 definition
 Energy of:

Internal vibrations &

Random motions of:
 molecules and/or
 atoms w/
 Internal vibrations &

Random motions of:
 molecules and/or
 atoms w/
...in a system
 Heat energy
 Definition
 Where can Heat Energy come from? (2)
 Definition
 Where can Heat Energy come from? (2)
=energy dissapated as heat

Can come from:
 a collision
 a currentcarrying wire
(among other things)

Law of Conservation of Energy says...?
 in an isolated system:
 energy is ALWAYS CONSERVED
 e.g., it can be transferred, but never lost
 energy is ALWAYS CONSERVED
 e.g., it can be transferred, but never lost
 Define an "Open system"
 both mass AND energy

...can be exchanged with surroundings
 ...can be exchanged with surroundings
Define a "Closed system"

Energy, but NOT mass
 ...can be exchanged with the surroundings
 ...can be exchanged with the surroundings
 Define an "Isolated system"

Neither mass NOR energy

...can be exchanged with the surroundings
 ...can be exchanged with the surroundings
 Think of "Work" in what order?
 ...when it comes to formulas
 ...when it comes to formulas
 W=ΔE
 W=Fdcosθ
 When I see the following, Ill think "WORK"
 7 things
 7 things
 Change in velocity
 Change in height
 Change in positon of masses (or planets in space)
 Change in position of a charge

Compression of a spring (PE stored up)
 Friction
 Air resistance
 Give 2 examples of W=Fdcosθ
 aka...give 2 examples of force being applied along a displacement
 aka...give 2 examples of force being applied along a displacement
 Pushing a block along a table
 An object falling from height
 height=displacement!
 Dont forget that!
 height=displacement!
 Dont forget that!
 What are the ONLY 2 ways energy can be transferred in/out of a system?
 Work
 Heat (dissapated)
 1^{st} Law of Thermodynamics
 Equation=?
 Equation=?
ΔE= W + Q
 WorkEnergy theorem
 What should you focus on instead?
 What should you focus on instead?
 If F_{net} does work on a rigid object:
 the work done on that object is equal to:
 the change in KE of the object
 Focus on W=ΔE
 correct use of this negates need to use workenergy theorem
 the work done on that object is equal to:
 the change in KE of the object
 correct use of this negates need to use workenergy theorem