# Physics 106 Fall 2003 - PowerPoint

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```					      Topic Outline
for Physics 106 Students
(includes Physics 105)
Spring 2011

Spring 2011 1
Physics B (106) Course Overview
motion of point bodies
kinematics - translation
•PHYSICS A    dynamics
•COVERED:                      F     ext    ma
conservation laws: energy & momentum

motion of “Rigid Bodies” (extended, finite size)
rotation + translation, more complex motions possible
•PHYSICS B
• COVERS:     rigid bodies: fixed size & shape, orientation matters
kinematics of rotation
dynamics
F ext    macm and    ext    I
rotational terms for energy conservation
conservation laws: energy & angular momentum

•TOPICS:
8   weeks - rotation:                         •Angular versions of
2   weeks - gravitation                       • kinematics
2   weeks – oscillations                      • second law
1   week - fluids                             • angular momentum
1   week - Phys 105/106 review                • equilibrium

Spring 2011
Linear and Rotational Mechanics: Logical Structure

NEWTONIAN MECHANICS
NEWTON’S SECOND LAW
forces & torques cause
acceleration is proportional to net force
changes in the motion
IMPULSE-MOMENTUM
TRANSLATIONAL                 impulse changes the linear momentum
STATIC EQUILIBRIUM
DYNAMICS                                                                         linear and rotational
movement from one place to                  WORK-ENERGY                               accelerations are zero
another                  external work changes the total energy

ROTATIONAL                           NEWTON’S SECOND LAW
DYNAMICS                angular acceleration is proportional to net torque
rotation from one orientation
to another
IMPULSE-MOMENTUM
angular impulse changes the angular momentum

ROTATIONAL WORK-ENERGY
external work changes the total energy, including rotational KE

CONSERVATION LAWS
LINEAR MOMENTUM IS CONSERVED
some quantities remain constant
for isolated system of translating bodies
for an isolated system

ANGULAR MOMENTUM IS CONSERVED
TOTAL ENERGY IS CONSERVED                   for isolated system of rotating bodies
for isolated system of particles                                                    Spring 2011
Physics A (105) Topics - Checklist
Introduction to the course
One dimensional motion
• Introduction to motion & kinematics,
Measurement
definitions
• Measurements
• Position and displacement
• Systems of units
• Average velocity, average speed
• Conversion of units
• Instantaneous velocity and speed
Vectors
• Acceleration
• Vectors and scalars
• Constant accleration - a special case
• Kinematics equations
subtraction
• Free fall acceleration
• Components of vectors and
unit vectors                    • Constant acceleration (using
integrals).
components (analytic            Two and three dimensional motion
method)                         • Position and displacement
• Vectors and the laws of          • Average and instantaneous velocity
physics                         • Average and instantaneous
• Multiplying vectors:               acceleration
– Scalar multiplication        • Kinematic equations in 2 & 3 D
– Dot product                  • Projectile motion defined (free fall)
– Cross product (vector        • Projectile motion analyzed, range
product                     • Uniform circular motion
• Relative motion in one and two
dimensions          Spring 2011
Physics A (105) Topics - Checklist

Linear dynamics
Linear dynamics with friction
• Dynamics, some history
• Dynamics summary
• What causes an acceleration
• Friction basics
• Force                                    •   Static friction
• Newton’s first law                       •   Kinetic friction
• Where we can use the second         •   Properties of friction and sample
and third laws                         problems
• Mass                                •   Drag forces and terminal speed
• Newton’s second law
•   Free body diagrams           Uniform circular motion - centripetal
•   Some particular forces          force
•   Newton’s third law                     •   Free body diagrams
•   Application to sample problems         •   Sample problems with friction
•   Pulley problems
•   Block sliding problems
•   Simple block on plane with
friction
•   Simple equilibrium

Spring 2011
Physics A (105) Topics - Checklist
Potential energy and energy
conservation
Work and Energy
• Overview and summary
• Energy overview
• Potential energy
• Work
• Conservative forces
–   A simple constant force 1D
–   3D, constant force - dot product
• Determining potential energy
values
–   Units
–   Gravitational potential energy
–   Variable force 1D
–   Elastic potential energy
–   General vector 3D definition with
variable force                      •   Conservation of mechanical
•   Work and kinetic energy                      energy
–   Kinetic energy                      •   Reading potential energy curves
–   Simple derivation of work-ke             –   Energy levels
theorem                                  –   Finding the force (gradient)
•   General form of work-KE theorem               –   Turning points
•   Gravitational force and examples              –   Equilibrium points

•   Variable (spring) force and              •   Work done by external (non-
examples.                                    conservative) forces
•   Power                                    •   Work-energy theorem
•   Conservation of energy (general)
•   Isolated systems
•   Power
Spring 2011
Physics A (105) Topics - Checklist

Systems of particles, momentum      Impulse and collisions
• Center of mass                    • What is a collision?
–   Systems of particles       • Impulse and linear momentum
–   Solid bodies                    –   Single collisions
•   Newtons second law for a             –   Series of collisions
system of particles             •   Momentum and kinetic energy
•   Linear momentum                     in collisions
•   Linear momentum for a system    •   Inelastic collisions in one
of particles                        dimension
•   Conservation of linear          •   Elastic collisions in one
momentum                            dimension
•   Systems with varying mass (A    •   Collisions in two dimensions
rocket) - read only             •   Projectile collisions and
explosions

Spring 2011
Physics B (106) Topics - Checklist
Rotational variables, kinetic energy
• Translation and rotation
Angular momentum
• Rotational variables - kinematics of
• Rolling
rotation
• Kinetic energy and forces of rolling
–   Angular position and displacement
–   Angular velocity and acceleration   • Rotational quantities as vectors
•   Relating linear and angular variables    • Cross product revisited
rotation with constant angular           • Torque as a vector
acceleration                             • Angular momentum – conceptual
•   Kinetic energy of rotation               • Newton’s second law in angular form
•   Angular quantities as vectors            • Angular momentum as a vector
• Angular momentum of a system of
particles
• Angular momentum of a rigid body
Rotational inertia/moment of inertia
—   Particles and rigid bodies
• Conservation of angular momentum
–   Parallel axis theorem definition       for particles, rigid bodies, and systems
–   Proof of parallel axis theorem
–   Standard moments of inertia
Torque – rotational analog of force
— Moment arm for 2 dimensions
— Cross product, cross product review
Newton’s second law for rotation
Work and rotational kinetic energy

Spring 2011
Physics B (106) Topics - Checklist
Equilibrium                               Gravitation
• Overview - equilibrium defined          • Newton’s law of gravitation
(force)
• Conditions for equilibrium
• Gravitational field (acceleration)
• Center of gravity
–   Definition
• Superposition
–   Finding it                       • Shell theorem
–   When do mass center and CG not   • Gravitational potential energy and
coincide?                           escape speed
•   Methods for equilibrium problems      • Kepler’s 3 laws: orbits, period,
•   Examples of static equilibrium           radius
problems                              • Satellites and planets
• Orbits and energy
Fluids
• Density, Pressure                       Oscillations
• Pressure variation with depth           • Simple harmonic motion
• Pascal’s principle                      • X(t), v(t), a(t) as trig functions
• Devices                                 • The spring oscillator and the force
• Buoyant forces                             law for simple harmonic motion
• Archimedes principle                    • Kinetic and potential energy
• Fluid dynamics assumptions              • SHM: torsion pendulum, simple and
• Mass flow rate (flux)                      physical pendula
• Continuity Equation                     • Damped and forced oscillations,
• Bernoulli’s Equation (optional)            resonance             Spring 2011

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