Trigonometry-Based Physics I — Master Video List

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Module 1: Measurement and Units

Lecture Videos: 

Scientific Notation, Units and Significant Digits

• *Scientific notation review [2021.08.14]
• *SI prefixes [2021.08.16]
• *Units of volume and conversions [2021.08.16]
• *Example:  unit conversion (speed of light in mi/hr) [2021.08.17]
• *Example: unit conversion (density of gold conversion) [2021.08.17]
• *Example:  unit conversion (seconds in a year) [2021.08.17]
• *Example:  unit conversion (miles in a light year) [2021.08.17]
• *Significant digits:  addition and subtraction [2021.08.18]
• *Significant digits:  multiplication and division [2021.08.18]
• *Propagation of error (important for lab 1 calculations!) [2021.08.19]

Additional Examples (previous quiz and test items):

• *Example:  number of football fields to cover the Earth [2023.11.02]
• *Example:  number of football fields along the equator [2023.08.25]
• *Example:  moment of inertia error propagation problem [2022.09.27]
• *Example:  propagation of errors with spring potential energy formula. [2022.08.28]
• *Example:  unit conversion and significant digits (energy of a free proton) [2022.06.16]
• *Example:  density of the moon [2022.03.21]
• *Example:  volume of a cylinder/propagation of error [2022.03.21]
• *Example:  area of a rectangular property using propagation [2022.02.27]
• *Example:  atoms of gold in one ounce [2022.02.07]
• *Example:  significant digits/unit conversion (volume) [2021.10.14]
• *Example:  propagation of error (centripetal acceleration) [2021.10.14]
• *Example:  significant digits (wave velocity) [2021.09.17]
• *Example:  propagation of error (kinetic energy) [2021.09.17]

Module 2: One-Dimensional Kinematics

Lecture Videos: 

Introduction to 1D Kinematics:

• *Position time graphs and slope, velocity time graphs and area [2021.08.27]
• *Velocity time graphs and slope, acceleration time graphs and area [2021.08.27]
• *Measuring speed with an iPhone [2021.02.07]
• *Optional Derivation: Derivative and integral relations between position, velocity and acceleration + examples. [2021.08.29]
• *Deriving the equations for constant acceleration kinematics + examples. [2021.08.29] (note:  can skip the calculus here, but make sure to view the examples in the last video chapter)
• *Common mistakes in physics:  area bounded by a velocity time graph [2023.08.29]
• *Short animation:  animating motion on an x-t graph and in a 1D space simultaneously [2023.09.01]
• *Short animation:  animating motion on a v-t graph and in a 1D space simultaneously [2023.09.01]

Additional Examples (previous quiz and test items):

• *Example:  free fall on the moon, feather and hammer experiment [2023.09.29]
• *Example:  minimum acceleration to avoid a collision [2023.08.29]
• *Example:  displacement and average velocity from a v-t graph [2023.08.27]
• *Example:  vertical free fall from rest, flight time and final speed [2023.08.25]
• *Example:  two rocks dropped from a building [2022.09.30]
• *Example:  a-t graph with a short burst of acceleration [2022.09.28]
• *Example:  given v-t data, estimate displacement and acceleration. [2022.08.29]
• *Example:  car accelerates then brakes to a stop, find max speed and total displacement. [2022.06.27]
• *Example:  v-t graph for constant negative acceleration, make an a-t graph and find avg. velocity. [2022.06.24]
• *Example:  v-t graph, displacement and average velocity [2022.03.22]
• *Example: vertical free-fall upward launch, height and speed [2022.03.22]
• *Example (pebble launched downward from a bridge) [2022.02.07]
• *Example (sinusoidal position-time graph: speed and velocity) [2022.02.07]
• *Example:  v-t graph, find inst. acceleration and average velocity. [2021.10.14]
• *Example:  car brakes, then coasts, find the displacement [2021.10.14]
• *Example:  position-time graph, compute velocity and avg. velocity. [2021.09.17]
• *Example:  block sliding down ramp, find a given displacement and final speed. [2021.09.17]
• **Example:  two objects in vertical free fall, height and time when they pass. [2021.09.17]
• *Example:  displacement and average velocity from a v-t graph. [2021.04.24]
• *Example:  position and time for two cars to pass. [2021.04.24] 
• *Example:  displacement vs. distance, average velocity vs. speed. [2021.03.06]
• *Example:  car slowing to a stop. [2021.03.06]
• *Example:  acceleration of a bullet hitting a tree. [2021.03.06]
• *Example:  vertical free fall + time to hear the crash. [2021.03.06]
• *Example:  two cars crash. [2021.03.06]

Module 3: Vectors and Projectile Motion

Lecture Videos: 

Vectors:

• *Introduction to vectors and geometric vector addition. [2021.08.21]
• *Vector components introduction and examples. [2021.08.21]
• *Quantitative vector addition using components. [2021.08.22]

Kinematics in 2D:

• *How the acceleration vector affects the velocity vector. [2021.09.05]

Projectile Motion:

• *Non-calculus derivation of the equations of motion for projectile motion + example with flight time and range. [2021.09.06]
• *Animation and description of vectors in projectile motion [2023.09.22]
• *Short animation of vectors in projectile motion [2023.09.22]
• *How to compute the impact velocity of a projectile [TBA]
• *Proving that projectile motion is parabolic [TBA]
• *Example: Projectile flight terminates at a known value of x, and compute the impact velocity. [2021.06.15]
• *Example: Projectile motion with object landing higher than the launch. [2021.03.08]
• *Example: Projectile motion with a horizontal launch from a height (related to this week's lab). [2021.03.07]

Relative velocity:

• *Derivation of relative velocity formula, with airplane example [2022.09.01]

Additional Examples (previous quiz and test items):

• *Example:  projectile motion, golf shot on the moon [2023.09.30]
• *Example:  find the range for a thrown baseball [2023.09.14]
• *Example:  projectile motion, object lands on the roof, get time, range, impact speed [2022.10.03]
• *Example:  projectile launched horizontally, use range to find the speed [2022.09.23]
• *Example:  another projectile across a canyon into a vertical face. [2022.05.27]
• *Example: addition of force vectors by components [2022.03.23]
• *Example: projectile motion launch from a cliff, max height, flight time, impact angle [2022.03.23]
• *Example (projectile with horizontal launch, unknown height) [2022.02.17]
• *Example:  projectile launched across a canyon into vertical face. [2021.10.15]
• *Example:  relative velocity with a boat crossing a river. [2021.09.27]
• *Example:  Projectile motion initial downward y-velocity component. [2021.09.27]
• *Example: Projectile with tilted launch from a cliff. [2021.04.25]
• *Example:  projectile launch on a level surface, flight time, max height, etc. [2021.03.23]

Module 4: Introduction to Newton's Laws

Lecture Videos: 

Newton's First Law (N1):

• Introduction to Newton's First Law [TBA]
• Application of Newton's First Law [TBA]

Newton's Second Law (N2):

• *Introduction to Newton's second law:  why F=ma + two examples [2022.09.03]
• *Mass, weight and normal force + three examples [2022.09.04]
• *Normal force on a tilted surface, components of the weight vector + inclined plane example [2022.09.05]
• *Short animation:  a trick for finding vector components on an incline [2022.09.06]
• *Example:  mass suspended from three strings [2022.09.08]
• *Example:  horizontal Atwood machine, find acceleration and tension [2023.09.04]
• *Example:  normal force on an elevator ride [2022.09.25] [link to cquiz]
• *Common mistake: vector magnitudes don't add! [2023.09.09]
• *Common mistake: five examples where normal force is not mg. [2023.09.10]
• *Common mistake: T is not mg in an accelerating Atwood machine [2023.09.10]

Newton's Third Law (N3) and review of N1-N3:

• Newton's Third Law Intro [TBA]
• *Quick summary of Newton's Laws (old video) [replace]

Additional Examples:

• *Example:  tilted Atwood machine, no friction [2023.10.04]
• *Example:  two blocks accelerated vertically, given the breaking strength of the strings [2023.09.30]
• *Example:  pushing three blocks on a smooth surface [2023.09.16]
• *Example:  atwood machine with masses of 2M and 3M [2022.10.04]
• *Example:  find the third force to balance the first two (2D) [2022.10.01]
• *Example: block dragged by a rope, including friction [2022.03.24]
• *Example: inclined Atwood machine with M and 2M [2022.03.24]
• *Example (scale on an elevator stationary vs. accelerating) [2022.02.17]
• *Example:  two blocks on a level surface, N2 and N3 questions. [2021.09.27]
• *Example: Atwood sliding at constant speed due to friction. [2021.09.27]
• *Example: vertical Atwood, acceleration and kinematics question. [2021.09.27]
• *Example:  change in velocity and position from a constant force-time graph. [2021.06.14]
• *Example:  pushing a combination of blocks. [2021.04.25]
• *Example:  car braking to a stop, force given. [2021.03.23]
• *Example:  level surface, rope pulling up at an angle. (old video) [2020.09.25]
• *Example:  a block sitting on a block. (old video) [2020.09.15]
• *Example: an applied force with a downward component. (old video) [2020.09.15]
• *Example:  Horizontal Atwood Machine (old video) [2020.09.11]
• *Example:  Tilted Atwood Machine (old video) [2020.09.11]

Module 5: Applications of Newton's Laws

Lecture Videos: 

Miscellaneous Dynamics Problems

• *Introduction to equilibrium. (old video) [2020.09.20]
• *Example:  an object suspended from strings (note this is part of a larger video and you can ignore the torque problem). [2020.11.08]
• *Example:  sliding down an incline with constant velocity. (old video) [2020.09.22]
• *Example:  angle of tilt for fuzzy dice in an accelerating car. (old video) [2020.09.22]

Problems with Static and Kinetic Friction

• Introduction to static and kinetic friction [TBA]
• *Example:  given velocity time data for a slide to a stop, find coefficient of friction [2023.10.02]
• *Example:  pushing down at an angle on a block, with friction [2023.10.03]
• *Example:  sliding up and down the ramp with friction, round trip travel time, etc. [2022.10.06]
• *Example: kinetic friction speeds up a sliding box! [2022.06.13]
• *Example:  four blocks dragged at constant speed with friction [2022.05.30]
• *Example:  horizontal Atwood with block stacked on the cart, misc. questions. [2021.10.15]
• *Example:  block sliding down a ramp with friction, acceleration is known, misc. questions. [2021.10.15]
• *Example:  two blocks with friction, sliding at constant velocity, find the coefficient of kinetic friction. [2021.06.16]
• *Example:  Tilted Atwood machine with friction. [2021.04.25]
• *Example:  Atwood machine with static and kinetic friction. [2021.04.07]
• *Example:  breakaway force and acceleration of a block with friction. [2020.09.22]
• *Example:  breakaway force when the force is pulling up at an angle. [2020.09.22]
• *Example [related to lab]:  breakaway force. [2020.09.22]
• *Example [related to lab]:  breakaway angle for a block on a ramp. [2020.09.22]
• *Example [related to lab}:  sliding to a stop. [2020.09.22]
• *Example [related to lab]:  block sliding on an inclined plane with friction. [2020.09.22]

Module 6: Modules 1–5 Exam

Note: most past exam material (2020 - 2023) has been folded into the "additional examples" videos in the prior modules. Actual exams and video solutions (2024 - present) will be provided here [TBA]

Module 7: Uniform Circular Motion and Gravitation

Lecture Videos: 

Circular Motion Kinematics

• Angular speed and angle as a function of time for uniform circular motion. [2022.08.30]
• The relationship between linear and angular velocity.  [2022.08.30]
• Derivation of the equations of motion for UCM + the centripetal acceleration formula [2022.08.30]
• *Short:  converting RPM to radians/second. [2022.09.06]
• *Example: angular velocity, period and frequency of rotation.  [2020.10.05]
• *Example:  rotations per minute to radians per second, tangential velocity, centripetal acceleration.  [2020.10.07]
• *Example:  compute the centripetal acceleration and tangential velocity at the edge of a disk. [2020.10.05]

Circular Motion Dynamics

• *Introduction to centripetal force + the simplest UCM problem.  [2020.09.24]
• *Example:  UCM on a vertical path.  [2020.10.22]
• *Example: find the minimum speed to make it through a loop. [2020.10.11]
• *Example:  UCM at an angle (conical pendulum)  [2020.09.23]
• *Example:  measure the mass of a stopper using UCM.  [2020.10.07]
• *Example:  car rounding a curve, relying on friction.  [2020.09.24]
• *Example:  banked turn, perfect speed and angle to avoid friction.  [2020.09.24]

Gravitation

• *Introduction to Newton's Law of Gravitation, the Cavendish experiment, and an example. [2021.10.06]

Additional Examples

• *Example: tension at the top and bottom of a vertical loop [2023.11.03]
• *Example: maximum speed for a car rounding a corner on a level surface [2023.10.10]
• *Example: rotating swing ride problem [2022.11.23]
• *Example:  weighing the Sun using Jupiter's orbit [2022.10.15]
• *Example:  maximum height before pendulum string breaks. [2022.05.06]
• *Example: Breaking strength of a string in UCM. [2022.04.02]
• *Example:  orbital period and speed of the LRO lunar orbiter probe. [2022.04.03]
• *Example:  car rounding a corner, find the angle of the fuzzy dice. [2020.11.25]
• *Example:  apparent weight at the equator. [2021.04.25]
• *Example:  space station artificial gravity. [2021.11.24]
• *Example: Weighing the Sun [2020.10.05]

Module 8: Work and Energy

Lecture Videos: 

Work and Kinetic Energy

• *Definition and units of work:  constant force and direction case (no calculus) [2020.10.06]
• *Where does the formula for kinetic energy come from?  Derivation of work-energy theorem. (optional: uses calculus) [2020.10.06]
• *Why is work defined this way?  Path independence of gravity example. [2020.10.06]
• *Forces of constraint do no work. [2020.10.06]
• *Cumulative Example: final velocity from a force-position graph + kinematics question [2022.05.26]
• *Example:  work done by applied force and friction for a sliding block. [2020.11.25]
• *Example:  work done by tensions in a sliding block problem. [2020.10.22]
• *Example:  work done by two forces at constant velocity + work done by friction. [2021.10.30]
• *Example:  block sliding down a ramp at constant speed, work done by friction. [2020.10.22]

Power

• *Introduction to power, examples, power vs. time graphs, constant velocity formula. [2021.10.05]

Conservative Forces, Potential Energy and Conservation of Energy

• *Where does the formula for kinetic energy come from?  Derivation of the work-energy theorem. (optional:  uses calculus) [2020.10.06]
• *Potential energy and the work done by gravity. [2020.10.11]
• *Potential energy and the work done by a spring. (optional: uses calculus) [2020.10.11]
• *Quick proof of conservation of energy, with and without friction. [2020.10.11]
• Force in Hooke's Law springs.[TBA]
• *Example:  work done by a Hooke's Law spring vs. work done on a Hooke's Law spring (optional: uses calculus) [2020.10.06]

Additional Examples (previous quiz and test items)

• *Example: block landing on a spring, maximum compression [2023.11.04]
• *Example: work done by static friction while a car brakes [2023.11.03]
• *Example: block pulled up at an angle net work and final speed with friction [2023.10.11]
• *Example: block shot up a ramp by a spring [2022.11.24]
• *Example:  spring launches a block that later slides to a stop on a rough surface [2022.10.15]
• *Cumulative Example:  block runs into a spring, find the maximum compression and maximum acceleration. [2022.08.05]
• *Example:  block pulled by a string at an angle with friction: get the final speed using work approach. [2022.06.29]
• *Cumulative Example:  another pendulum with energy conservation and circular motion [2022.05.31]
• *Example:  maximum compression of a spring (symbolic) with and without friction. [2022.05.08]
• *Cumulative Example:  maximum height before pendulum string breaks. [2022.05.06]
• *Example: Spring gun, potential energy, spring constant and average power output. [2022.04.03]
• *Example:  sliding down a ramp with friction, work done by gravity and friction [2021.11.22]
• *Cumulative Example:  energy conservation with circular motion, object rolls into a bowl. [2021.11.21]
• *Cumulative Example:  energy in a spring gun for projectile + projectile motion. [2021.10.30]
• *Cumulative Example:  pendulum speed at the bottom and tension at the bottom. [2021.06.17]
• *Example:  block sliding down a ramp into a spring. [2021.04.30]
• *Cumulative Example:  uniform circular motion with a spring. [2021.04.07]
• *Example:  car with a springy bumper, find the maximum compression and acceleration. [2020.11.25]
• *Example:  net work and kinetic energy for a sliding block. [2020.11.05]
• *Example:  roller coaster through the loop (much greater than the minimum speed). [2020.10.22]
• *Example:  roller coaster through the loop (minimum height to make it through the loop) [2020.10.15]
• *Example:  three projectiles launched with the same initial height and speed. [2020.10.11]
• *Example:  spring shooting a mass horizontally. [2020.10.11]
• *Example:  spring shooting straight up. [2020.10.11]
• *Review Example: find the minimum speed to make it through a loop. [2020.10.11]
• *Example:  conservation of energy, including spring energy and friction. [2020.10.11]
• *Example:  horizontal spring launch with friction. [2020.10.11]

Module 9: Momentum

Lecture Videos: 

Momentum and Collision Problems:

• *Definition of momentum and impulse + a quick example. [2020.10.19]
• *Momentum and its relation to force + average force example. [2020.10.19]
• *Example:  impulse from a force-time graph.  Find the final speed and the work done. [2020.10.19]
• *Why is momentum conserved?  Quick derivation starting from Newton's third law. [2020.10.19]
• *Example:  perfectly inelastic collisions and illustration that energy must be lost. [2020.10.19]
• *Example:  perfectly elastic collisions. [2020.10.19]

Additional Examples (previous quiz and test problems):

• *Example: head-on perfectly inelastic collision [2023.11.05]
• *Example: dart impacts a block connected to a spring [2022.12.01]
• *Example: impulse and average force for a ball bouncing off a wall. [2022.11.19]
• *Example:  two masses M and 2M spring apart with energy E [2022.11.01]
• *Cumulative Example:  moving blocks spring apart, find the final speed and initial spring energy. [2022.08.10]
• *Cumulative Example:  inelastic collision with friction before and after the collision. [2022.06.01]
• *Cumulative Example:  pendulum partially elastic collision. [2022.05.10]
• *Cumulative Example:  fan cart work, power, impulse, average force. [2022.05.09]
• *Example: clay blob used to stop a block [2022.04.21]
• *Cumulative Example:  spring gun recoil used to move a cart. [2021.11.28]
• *Example: hay bail dropped vertically into a moving cart. [2021.11.08]
• *Example:  multiple inelastic collisions. [2021.06.19]
• *Example:  final velocities for masses pushed apart by a coiled spring. [2021.06.18]
• *Example:  rubber ball shot at a cart. [2021.05.01]
• **Example:  velocity after n inelastic collisions. [2020.11.27]
• **Cumulative Example:  the ballistic pendulum. [2020.11.25]
• *Example:  2D inelastic collision. [2020.10.23]
• **Example:  compute the maximum compression of a spring during a collision. [2020.10.23]
• *Example:  an explosion with known energy -- what percent of energy goes into each piece? [2020.10.22]

Module 10: Rotational Kinematics and Dynamics

Lecture Videos: 

Rotational Kinematics and Rotational Energy

• Review: *Angular speed and angle as a function of time for uniform circular motion [2022.08.30]
• Review:  *The relationship between linear and angular velocity [2022.08.30]
• Review:  converting RPM to radians/second. [2022.09.06]
• *Rotational variables and constant angular acceleration equations + example [2020.11.02]
• *Relating linear and angular speed and acceleration + example. [2020.11.02]
• *Example:  a grinding wheel slowing to a stop. [2020.11.02]
• *Rotational energy and moment of inertia derivation + example. [2020.11.02]
• *Example:  rotational kinetic energy of the Earth. [2020.11.02]
• *Example:  conservation of energy -- disk with a falling mass. [2020.11.02]
• *Example:  conservation of energy -- Atwood machine with a heavy pulley. [2020.11.02]
• *Example:  work and energy -- spinning up a disk using a string wrapped around the hub (related to lab) [2020.11.02]

Torque and Angular Acceleration

• *Defining torque + simple examples. [2020.11.03]
• *The rotational analogue to N2:  torque causes angular acceleration. [2020.11.03]
• *Example:  same disk from work/energy example, but solve it using torque and angular acceleration (related to lab) [2020.11.03]
• *Example:  grinding wheel slowed by friction. [2020.11.03]
• *Example:  disk accelerated by pulling a string:  torque, angular acceleration, kinetic energy (related to lab) [2020.11.25]

Torque Due to Gravity + Gravitational PE for a Rigid Body

• *Gravitational potential energy for a rigid body + example. [2020.11.03]
• *Example:  torque exerted by gravity on a horizontal rod attached to a hinge. [2020.11.03]

Additional Examples (previous quiz and test items)

• *Example: rotational Atwood machine, energy approach [2023.11.07]
• *Example:  accerating heavy disk, power and time given, compute average torque [2023.10.27]
• *Example:  disk accelerated by a string wrapped around a hub. [2022.11.22]
• *Example:  motor accelerates from rest to 2000RPM in 0.5s. [2022.11.03]
• *Example:  ramp atwood - unwinding a heavy pulley. [2022.05.17]
• *Example: disk accelerated by a motor:  final speed, average acceleration and torque [2022.04.21]
• **Example: two pulleys with hanging masses going opposite directions (force/torque analysis) [2022.06.09]
• *Example:  average torque and power output for a motor accelerating a heavy disk. [2022.06.02]
• *Example:  ceiling fan rotational acceleration, speed, average power [2021.11.08]
• *Example:  heavy disk slows to a stop, torque and work due to friction. [2021.06.20]

Module 11: Wrapping Up Rigid Body Dynamics + Static Equilibrium

Lecture Videos: 

Energy in Combined Rotation and Translation

• *Statement of total energy of an object with both translation and rotation (no derivation) + simple example. [2020.11.06]
• *Condition for rolling without slipping + application to a rolling ball (% energy) [2020.11.06]
• *Example:  ball vs. disk rolling down a hill, energy approach [2020.11.06]
• *Example:  ball rolling down a hill. [2020.11.25]
• *Example:  disk rolling along an axle, translational and rotational energy [2021.11.25]

Angular Momentum

• *Angular momentum and conservation for pure rotation + simple example (kid on a merry-go-round) [2020.11.06]
• *Example:  revolving mass on a table top pulled to a smaller radius [2020.11.07]

Static Equilibrium

• *Conditions for static equilibrium + 2 simple examples (point mass vs. extended object suspended from strings) [2020.11.08]
• *Example from lab:  mass suspended from strings + law of cosines [2020.11.08]
• *Example from lab:  balancing point for a rod and mass system [2020.11.08]
• *Translating a force vector to compute torque (useful short cut!) [2020.11.18]
• *Example:  cat on a table, compute forces on the legs. [2020.11.18]
• *Example:  horizontal beam:  tension and force exerted by the hinge. [2020.11.18]
• *Example:  angled beam:  tension and force exerted by the hinge. [2020.11.18]

Additional Examples (previous quiz and test items)

• *Example: horizontal beam supported by a hinge and vertical string [2023.11.11]
• *Example: disk dropped on a rotating disk rotational collision [2023.11.10]
• *Example: max height for a solid ball rolling up a hill, energy approach [2023.11.09]
• *Example:  beam suspended by two vertical cables. [2022.11.23]
• *Example: hollow ball rolls without slipping down a ramp [2022.11.28]
• *Example:  beam and cable problem with horizontal beam, tilted cable, and additional hanging mass. [2022.08.12]
• *Example:  retracting masses on a rotating disk. [2022.05.11]
• *Example:  ring rolling down an incline. [2022.05.06]
• *Example:  mechanical advantage of a post jack. [2021.11.28]
• *Example:  horizontal rod with a hinge at the center. [2020.11.25]
• *Example:  angular momentum conservation:  first approximation of white dwarf spin rate [2020.11.07]

Module 12: Modules 7-11 Exam

Note: most past exam material (2020 - 2023) has been folded into the "additional examples" videos in the prior modules. Actual exams and video solutions (2024 - present) will be provided here [TBA]

Module 13: Fluids

Lecture Videos: 

Fluid Statics

• *Density + examples.
• *Pressure as force per unit area + examples.
• *Quick note on absolute vs. gauge pressure.
• *Pressure at depth in a fluid + example.
• *Example:  pressure from a water tower.
• *Example:  open-tube manometer.
• *Example:  how a hydraulic jack works.
• *Example:  how a siphon works.
• *Buoyancy:  Archimedes' principle and two examples (floating glacier ice, apparent weight of a basalt cobble).

Fluid Dynamics

• *Continuity equation for a nearly incompressible fluid.
• *Pressure as energy density + microscopic view of what's going on.
• *Bernoulli's equation.
• *Example:  water tower hydrostatic pressure and water velocity at a faucet.
• *Example:  water flow meter based on Bernoulli's equation.

Additional Examples (previous quiz and test items):

• *Example:  finding the density of a submerged rock. [2024.06.10]
• *Example: density of a submerged rock. [2022.05.12]
• *Example:  another venturi flow meter, using open manometers for the pressure.
• *Example:  continuity equation for a pipe that splits into two pipes, symbolic solution.
• *Example:  water column with a metal weight at the top, pressure + fluid velocity
• *Example:  pump gauge pressure required to draw bubbles from a submerged tube.

Module 14: Oscillations

Lecture Videos: 

Simple Harmonic Oscillations

• *Introduction to the simple harmonic oscillator + example. [2020.12.01]
• *Example:  phase space diagram for the simple harmonic oscillator. [2020.12.01]
• *Introduction to the simple pendulum and example. [2020.12.01]

SHO animations

• *Animation: energy in the simple harmonic oscillator [TBA]
• *Animation: oscillations and phase space [TBA]
• *Animation: SHO and the relation to uniform circular motion [TBA]

(optional) misc. calculus derivations for SHO and simple pendulum

• *Potential energy and the work done by a spring. [2020.10.11]
• *Derivation of equations of motion for the simple harmonic oscillator. [2020.12.11]
• *The phase angle form of the general solution + example. [2020.12.11]
• *Expanding the sine function in a power series (important for the derivation below). [2020.11.30]
• *Derivation of equations of motion for the simple pendulum. [2020.12.11]

Additional Examples (previous quiz and test items)

• *Example:  amplitude and maximum speed of an oscillator given total energy.  [2024.06.24] 
• *Example: spring constant and period for a mass hanging on a spring. [2022.05.13]
• *Example:  amplitude and maximum speed given initial position and velocity. [2021.06.22]
• *Cumulative Example:  inelastic collision with a harmonic oscillator. [2021.12.08]
• *Example:  spring constant and frequency of oscillation given the force to displace a mass from equilibrium. [2022.06.06]
• *Cumulative Example:  block runs into a spring, find the time for the bounce and the average force exerted. [2022.08.08]

Module 15: Mechanical Waves

Lecture Videos: 

Waves and Waves on a String

• *Frequency, wavelength, amplitude and wave speed. [2020.12.09]
• *Tension, linear density and wave speed on a string + example. [2020.12.09]
• *Fixed and free reflections, superposition principle., constructive/destructive interference. [2020.12.09]
• *Resonance for a string clamped at both ends + driving at a resonant frequency. [2020.12.10]
• *Example:  another resonance example for a string - many frequencies superposed. [2020.12.10]
• *Example:  resonance on a string, find the 2nd harmonic based on the 3rd harmonic. [2021.06.23]
• *Example:  wave speed and tension given the linear density and frequency of the 5th harmonic. [2022.06.07]
• *Example:  given two normal modes on a string, compute the fundamental harmonic, wave speed and tension. [2022.08.17]

Transverse Wave Animations

• *Animation: Math lesson: how to make a wave move to the left and right. [2021.10.02]
• *Animation: Wave reflections:  fixed end vs. free end, fast to slow transitions vs. slow to fast transitions. [2021.10.25]
• *Animation: Constructive and destructive interference, and formation of standing waves on a string. [2021.11.19]
• *Animation: Standing waves on a guitar string and superposition of normal modes. [2021.10.09]

Module 16: Sound and Hearing

Lecture Videos: 

Introduction to Sound Waves

• *Introduction to sound waves, pressure and displacement amplitude and the speed of sound. [TBA]
• *Sound intensity and the decibel scale. [2025.01.26]
• *Introduction to the Doppler effect [2023.01.31]
• *Resonance in a column of air [TBA]
• *Introduction to Acoustic Beats. [2025.01.24]
• *Shock waves, the sonic boom and the angle of a shock wave cone. [2025.02.08]

Additional Wave Animations

• *Animation:  plane traveling at Mach 2.0 [2025.02.08]
• *Animation:  plane traveling at Mach 1.2 [2025.02.07]
• *Animation:  plane traveling at Mach 1.0 [2025.02.07]
• *Animation:  plane traveling at Mach 0.8 [2025.02.07]
• *Animation:  Beats illustration: overlapping waves arriving at the ear + composite wave arriving at the ear.  [2025.01.25]
• *Animation:  Doppler effect for a stationary source and moving listener [2023.01.29]
• *Animation:  Doppler effect for a moving source and stationary listener [2023.01.29]
• *Animation:  Sound wave interference:  acoustic beats. [2021.10.19]
• *Animation:  The sound barrier, shock waves and sonic booms [2023.02.04]
• *Animation:  spatial interference of light waves (sound is totally analogous if two speakers emit a tone!) [2021.08.03]
• *Animation:  longitudinal vs.transverse waves.
• *Animation: surface waves in water (combination of transverse and longitudinal)
• *Animation: Rayleigh waves in an earthquake.