Significant Mechanics Equations

  • Displacement
  • Average velocity
  • Average speed
  • Instantaneous velocity

Graphs!!!

  • Instantaneous acceleration

average acceleration is secant line... algebra!

  • Constant acceleration equations
  • Projectile Motion For max range off a cliff, angle is less than 45 degrees
  • Circular Motion
  • Newton
  1. Inertia (rest or constant velocity)

2. (object or system of objects)

3. ActionReaction (touching or stacked blocks)

  • Weight

depends on location/planet

  • Friction
  • Work

hanging rope dF=λgdy

  • Potential Energy
  • Conservation of Mechanical Energy

If nonconservative forces

  • Power

Rate of energy transfer

  • Center of mass
  • Momentum
  • Collisions

then

Elastic : Momentum and Energy is conserved!

v1i+v1f=v2i+v2f

Inelastic: only momentum conserved!

Completely inelastic: momentum conserved but max

  • Impulse

Impulse increases when object bounces due to change of direction

  • Rotation

Tangential displacement

Tangential acceleration and angular acceleration are zero if angular velocity is constant

  • Constant angular acceleration equations
  • Moment of inertia

disk or cylinder: Rod:

  • Angular Momentum

then

If pinned down means linear momentum not conserved, but no net external torque means angular momentum is conserved

  • Torque
  • Rotational Kinetic Energy
  • Rolling

pure rolling: f(R)=Iα could be tension instead of friction

down Incline: mgsin a=Rα

slipping f=-ma

  • Work
  • Power
  • Static Equilibrium

Hanging signs, ladders

  • Gravity

Kepler 1. Elliptical orbits, sun/planet at focus (faster sun/planet at near focus, slower sun/planet at far focus)

  1. Radius vector sweeps out equal areas in equal times mvr=mvr
  • Gravitational Potential Energy
  • Escape velocity
  • Newton’s Universal Law of Gravitation

R=radius of circle r=center to center Inside planet R= Radius of Planet

  • Acceleration due to gravity
  • Oscillations

Definition of simple harmonic motion

  • Energy
  • Pendulum

Electricity and Magnetism Significant Equations

Point Charges

  • Coulomb’s Law: Force between two charges
  • Force on a point charge due to Electric Field

N/C or V/m

  • Gauss’s Law

Subtract for empty space A=2 A=4r2

  • Electric Potential Energy due to electric field
  • Electric Potential Energy between charges
  • Work to bring charge distribution together
  • Electric Potential due to Electric Field (Constant inside conductors)

: start at infinity: If constant E then

  • Electric potential due to a point charge

(equipotential lines=circles around a point charge, scalar...add!)

  • Electric potential due to many point charges
  • Capacitance

Farads dielectric

  • Energy stored in capacitors
  • Parallel Plate

This is true only because E=uniform between plates

Battery connected Voltage doesn’t change

Battery not connected charge on capacitor doesn’t change

  • Capacitors in Series
  • Cylindrical/spherical capacitors

(outside in)

  • Electric Current
  • Current Density

used for Ampere's Law

  • Drift velocity
  • Ohm’s Law
  • Resistivity
  • Power

Watts (rate of energy) Energy =

  • Resistors in Parallel
  • Resistors in Series
  • Kirchhoff Rules
  • RC charging( graphs!!! initially capacitor acts like a wire)

i=dq/dt

  • RC discharging (maintain voltage)( graphs!!! initially capacitor acts like battery)
  • Magnetic Force on a point charge due to a magnetic field
  • Magnetic force on a wire due to a magnetic field

: electric motors

  • Magnetic force between two wires

currents the same direction attract

  • Velocity selector

mass spectrometers

  • Torque on a loop due to a magnetic field

motors

  • Hall Effect- piece of metal/measuring voltage across, use left hand for electrons!!!
  • B-S Law (rings of wire)
  • Solenoid

: n= number of turns per unit length of solenoid

  • Ampere’s Law

inside vs. outside wires

  • Torrid

: N=number of turns

  • Magnetic Induction

Webers CALCULUS

  • Faraday’s / Lenz’s Law

ds=2πr : generators

  • Inductance
  • Inductor
  • (inductors maintain current)
  • Energy Stored in an inductor
  • LC circuit

Gauss’ Law

Gauss’ Law for Magnetism

Faraday’s Law

Ampere’s Law with Maxwell’s displacement current

  • Transformer

1. Design experiments

Students should understand the process of designing experiments, so they can:

a)Describe the purpose of an experiment or a problem to be investigated.

b)Identify equipment needed and describe how it is to be used.

c)Draw a diagram or provide a description of an experimental setup.

d)Describe procedures to be used, including controls and measurements to be taken.

2. Observe and measure real phenomena

Students should be able to make relevant observations, and be able to take

measurements with a variety of instruments (cannot be assessed via paper-and-pencil

examinations).

3. Analyze data

Students should understand how to analyze data, so they can:

a)Display data in graphical or tabular form.

b)Fit lines and curves to data points in graphs.

c)Perform calculations with data.

d)Make extrapolations and interpolations from data.

4. Analyze errors

Students should understand measurement and experimental error, so they can:

a)Identify sources of error and how they propagate.

b)Estimate magnitude and direction of errors.

c)Determine significant digits.

d)Identify ways to reduce error.

5. Communicate results

Students should understand how to summarize and communicate results, so they can:

a)Draw inferences and conclusions from experimental data.

b)Suggest ways to improve experiment.

c)Propose questions for further study.