-- KINEMATICS --

Kinematics – Lecture

26 Topics

P01-010 – Measuring Time & Position

P01-020 – Particle Model

P01-030 – Position Vector

P01-040 – Displacement Vector

P01-050 – Average Velocity Vector

P01-060 – Average Acceleration Vector

PNC-01-070 – Instantaneous Velocity

PNC-01-080 – Instantaneous Acceleration

P01-090 – Relationship Between Velocity & Acceleration

PNC-01-100 – Kinematic Equations with Constant Acceleration

P01-110 – Application: Free-Fall

P01-140 – Position Vector in 3D

P01-150 – Displacement Vector in 3D

P01-160 – Average Velocity Vector in 3D

P01-170 – Average Acceleration Vector in 3D

PNC-01-180 – Instantaneous Velocity in 3D

PNC-01-190 – Instantaneous Acceleration in 3D

P01-200 – Angular Position & Displacement

P01-210 – Average Angular Velocity

P01-220 – Average Angular Acceleration

PNC-01-230 – Instantaneous Angular Velocity

PNC-01-240 – Instantaneous Angular Acceleration

P01-250 – Relationship Between Angular Speed & Acceleration

PNC-01-260 – Kinematic Equations for Circular Motion

P01-270 – Relating Angular and Linear Quantities

P01-280 – Relative Motion in 2D

Kinematics – Problems

17 Topics

P01R2015 – Components & Dot Product

P01G2015 – Average Velocity

P01R2015 – Graphical Subtraction of Vectors

P01R2015 – Acceleration on an incline

P01R2015 – Vertical Free-fall

P01R2015 – Rising Rocket

P01G2019 – Rocket Launch

P01G2019 – Cars Racing Alongside Each Other

P01R2021 – Physics Rocks

P01R2015 – Catching the Bus

P01R2020 – Coming at Each Other

P01R2020 – Trains Crossing

P01R2015 – Highway Patrol

P01G2007 – Balls Colliding in Mid-air

P01G2008 – Passing a Car

P01R2015 – Furiously Fast

P01R2015 – Biking Along

-- PROJECTILE MOTION --

Projectile Motion – Lecture

7 Topics

P02-010 – Projectile Motion

P02-020 – Equations of Motion

P02-030 – Equation of the Path y = f(x)

P02-040 – Finding the Maximum Height

P02-050 – Property of the Path of the Projectile

P02-060 – Range of the Projectile

P02-070 – Launch Angle and Range Maximization

Projectile Motion – Problems

10 Topics

P02R2017 – Hats Off to Frosty

P02R2015 – Analysis of a Jump

P02R2015 – Hoop Spacing

P02G2018 – Air Drop

P02R2015 – A Ball Game

P02G2017 – Ball Toss

P02R2015 – Clearing the Edge of a Cliff

P02G2005 – Home Run

P02G2016 – Ball Thrown in the Air

P02S2010 – Tennis Ball Launcher and Mobile Target

-- NEWTON'S LAWS --

Newton’s Laws – Lecture

13 Topics

P03-010 – Force and Vector Representation

P03-020 – Common Forces: weight force

P03-030 – Common Forces: tension force

P03-040 – Common Forces: normal force

P03-050 – Common Forces: friction forces

P03-060 – Common Forces: spring force & Hooke’s Law

P03-070 – Free-Body Diagram

P03-080 – Net Force

P03-090 – Newton’s First Law

P03-100 – Newton’s Second Law

P03-110 – Newton’s Third Law

P03-120 – Application: ideal string

P03-130 – Application: ideal pulley

Newton’s Laws – Problems

22 Topics

P03G2018 – Blocks Slipping on an Incline

P03R2015 – Hanging Mass

P03R2015 – Keeping a Box at Rest

P03B2006 – Sliding or Not?

P03G2007 – Holding a Block on an Incline

P03G2008 – Holding a Block Up Against a Wall

P03G2016 – Pressing a Block Against a Wall

P03R2015 – Resting or Sliding Up an Incline

P03R2015 – Acceleration and Friction Forces

P03S2016 – Corvette Flying Off a Cliff

P03G2005 – Holding Up a Block

P03G2015 – Pushing on Three Blocks

P03S2016 – Pulling Stacked Blocks

P03R2015 – Blocks Sliding Down a Ramp

P03B2006 – Who is Pulling Who?

P03G2016 – Joint Inclines

P03G2017 – Pulling Three Blocks

P03G2018 – Pulling and Lifting

P03R2015 – Atwood Machine

P03R2015 – Acceleration Constraint

P03S2008 – Two Blocks on the Verge of Slipping

P03R2015 – Pulling Two Connected Boxes

-- CIRCULAR MOTION --

Circular Motion – Lecture

13 Topics

P04-010 – Circular Motion

P04-020 – RTZ Coordinate System

P04-030 – Direction of Acceleration

P04-040 – Components of Acceleration

P04-060 – Uniform & Non-Uniform Circular Motion

P04-070 – Period of Revolution

P04-080 – Newton’s Second Law

P04-090 – Angular Position & Displacement

PNC-04-100 – Instantaneous Angular Velocity

PNC-04-110 – Instantaneous Angular Acceleration

P04-120 – Relationship Between Velocity and Acceleration

PNC-04-130 – Kinematic Equations for Circular Motion

P04-140 – Relating Angular & Linear Quantities

Circular Motion – Problems

11 Topics

P04G2016 – Lift Force on a Plane

Interconnected Masses

P04B2006 – Space Ride

P04G2017 – Toy Car

P04G2018 – Holding a Block against a Wall

P04S2016 – Sliding Around a Funnel

P04S2016 – Pendulum on Planet Vulcan

Car Rounding a Curve

P04G2019 – Semicircular Hill and Valley

P04G2005 – Flying in a Loop

P04R2015 – Around the Loop

-- WORK & ENERGY --

Work & Energy – Lecture

12 Topics

P05-010 – Energy

P05-020 – Kinetic Energy

P05-030 – Gravitational Potential Energy

P05-040 – Elastic Potential Energy

P05-050 – Mechanical Energy

PNC-05-060 – Work Done by a Force

PNC-05-070 – Calculating the Work Done by a Force

PNC-05-100 – Work Done by the Weight Force

PNC-05-110 – Work Done by the Spring Force

PNC-05-120 – Work-Kinetic Energy Theorem

P05-140 – Conservation of Mechanical Energy

PNC-05-150 – Power and Mechanical Power

Work & Energy – Problems

16 Topics

P05D2015 – Spring Gun and Frictionless Track

P05G2007 – Package Landing on a Spring

P05S2016 – Sliding Over a Hill

P05G2019 – Block on a Vertical Spring

P05G2016 – Mass-Spring System

P05R2015 – Rough Sliding

P05G2017 – Shooting a Crate

P05G2018 – Back and Forth Between Springs

P05R2021 – Launching a Block Up a Rough Incline

P05S2016 – Sliding Down and Bouncing Back Up

P05S2015 – Sliding Across a Track

P05D2017 – Trapeze Artist and a Big Spring

P05G2019 – Pushing a Block on the Ceiling

P05G2018 – Projectile Launched from a Ramp

P05R2015 – Risky Swinging

P05B2018 – Loop-the-Loop

-- IMPULSE & MOMENTUM --

Impulse & Moment. – Lecture

10 Topics

P06-010 – Momentum Vector

PNC-06-020 – Newton’s Second Law in Momentum Form

P06-030 – Conservation of Momentum

PNC-06-040 – Impulse of a Force

PNC-06-050 – How to Calculate an Impulse

PNC-06-060 – Impulse-Momentum Theorem

P06-070 – Inelastic & Elastic Collisions

P06-080 – Solving Strategy: perfectly inelastic collision

P06-090 – Solving Strategy: head-on elastic collision

P06-100 – Solving Strategy: off-center elastic collision

Impulse & Moment. – Problems

13 Topics

P06G2005 – Game of Catch

P06G2019 – Blocks & Compressed Spring

P06B2006 – Saving Lois?

P06G2007 – Three Colliding Blocks

P06G2017 – Sequence of Collisions

P06R2019 – Two Collisions in a Row

P06R2015 – Ballistic Pendulum

P06G2016 – Collision Between Three Masses

P06G2018 – Masses Bouncing Off Each Other

P06R2015 – Blocks Colliding

P06R2015 – Explosion of a Hockey Puck

P06R2020 – Inelastic Collision vs. Elastic Collision

P06D2009 – Fun with a Slingshot

-- GRAVITATION --

Gravitation – Lecture

17 Topics

P07-010 – Gravitational Field

P07-020 – Gravitational Force

P07-030 – The Weight Force

P07-040 – The Principle of Superposition

P07-050 – Circular Orbits: uniform circular motion

P07-060 – Circular Orbits: orbital speed

P07-070 – Circular Orbits: period of revolution

P07-080 – Gravitational Potential Energy

P07-090 – Gravitational Potential Energy for a System of Masses

PNC-07-100 – Gravitational Potential Energy and Work

P07-110 – Conservation of Mechanical Energy

P07-120 – Nature of Orbits and Mechanical Energy

P07-130 – Escape Velocity

P07-150 – Kepler’s 1st Law: law of orbits

P07-160 – Kepler’s Second Law: law of areas

P07-170 – Kepler’s Third Law: law of periods for circular orbits

P07-180 – Kepler’s Third Law: law of periods for elliptical orbits

Gravitation – Problems

7 Topics

P07R2015 – Accelerations Due to Gravity

P07R2015 – Orbiting Satellite

P07R2015 – Geostationary Satellite

P07S2013 – Three Orbiting Bodies

P07S2013 – Orbiting the Center of Mass

P07R2015 – Satellite Orbiting Earth

P07R2015 – Of Kepler’s Laws

-- CENTER OF MASS --

Center of Mass – Lecture

5 Topics

P08-010 – Center of Mass of a System of Particles

P08-020 – Position of the Center of Mass

P08-030 – Velocity of the Center of Mass

P08-040 – Acceleration of the Center of Mass

P08-050 – Newton’s Second Law and Center of Mass

Center of Mass – Problems

10 Topics

P08R2015 – Walking to the End of the Canoe

P08D2014 – Elephant on a Train Car

P08R2015 – Collision and COM of Two Blocks

P08R2015 – Two Sliding Masses

P08R2015 – Two Sliding Masses at it Again

P08R2015 – COM of Three Boxes

P08G2019 – Stacked Blocks

P08R2015 – A Grenade Exploding in Midair

P08R2015 – Exploding Firework

P08S2015 – Jumping the Plank

MIDTERM 1 - STUDY GUIDE

Lowhorn – 8A 2018 Fall – Midterm 1 – L1

4 Topics

Multiple Choice Fall 2018

P02L2018 – Snowball Rolling Off a Roof

P03L2018 – Sliding from Under a Plank

P04L2018 – Banked Curve

Lowhorn – 8A 2019 Fall – Midterm 1 – L1

4 Topics

Multiple Choice Fall 2019

P02L2019 – Slanted Rocket Launch

P03L2019 – Sliding Connected Blocks

P04L2019 – Rotating Block with Two Strings

Lowhorn – 8A 2021 Spring – Midterm 1 – L1

4 Topics

P02L2021 – Lunch Throw

P03L2021 – Crate in a Truck Bed

P03L2021 – Stacked Blocks and Pulley

P04L2021 – Bead on a Rotating Ring

Lowhorn – 8A 2022 Spring – Midterm 1 – L1

4 Topics

P01L2022 – Kitty Kinematics

P02L2022 – Launching a Box Over a Ravine

P03L2022 – Unknown Suspended Mass

P04L2022 – Circular Hills and Valleys

-- SOLID ROTATION - STATICS --

Statics – Lecture

5 Topics

P09-010 – Equilibrium of an Extended Body

P09-020 – Introduction: three simple cases

P09-030 – Reminder: cross product of two vectors

P09-040 – Torque Created by a Force

P09-050 – Equilibrium Condition for an Extended Body

Statics – Problems

13 Topics

P09G2018 – Balanced Pole

P09R2015 – Ladder and Painter

P09R2015 – Resting Ladder

P09R2020 – Balanced Beam

P09S2016 – Balanced Sphere

P09R2015 – Straw Balanced Across a Glass

P09G2019 – Non-Uniform Hanging Bar

P09B2011 – Marble Quarry Crane

P09G2007 – Rod in Equilibrium

P09G2016 – Balancing a Horizontal Rod

P09G2017 – Two Balanced Rods

P09R2015 – Suspended Beam

P09R2020 – Balanced Beam with Hanging Mass

-- SOLID ROTATION - DYNAMICS --

Dynamics – Lecture

7 Topics

P10-010 – Solid Rotation

P10-020 – Angular Velocity Vector

P10-030 – Angular Acceleration Vector

P10-040 – Moment of Inertia

P10-050 – List of Moments of Inertia

P10-090 – Parallel-Axis Theorem

P10-100 – Newton’s Second Law for Rotational Motion

Dynamics – Problems

11 Topics

P10G2005 – Rotating a Disk and a Rod

P10G2016 – Rotating Cylinder

P10D2013 – Pushing a Dresser

P10D2013 – Wheel on a Hill

P10G2018 – Pushing a Door and a Box

P10R2015 – Kinematics of a Hollow Sphere

P10S2015 – Helicopter Blade

P10G2019 – Blocks & Non-ideal Pulley

P10G2007 – Pulley Lowering a Block

P10R2015 – Atwood Machine

P10B2018 – Block Lowered by a Pulley

-- SOLID ROTATION - ENERGY & MOMENTUM --

Energy & Moment. – Lecture

11 Topics

P11-010 – Angular Momentum

PNC-11-020 – Newton’s Second Law in Angular Momentum Form

P11-030 – Conservation of Angular Momentum

PNC-11-040 – Impulse-Momentum Theorem for Angular Momentum

P11-050 – Rolling Motion

P11-060 – Rolling w/o Slipping and Static Friction

P11-070 – Rotational Kinetic Energy

P11-080 – Rolling Kinetic Energy

PNC-11-090 – Work Done by a Torque

P11-100 – Work-Kinetic Energy Theorem

P11-110 – Conservation of Energy for Rolling w/o Slipping

Energy & Moment. – Problems

13 Topics

P11G2019 – Biking Down a Hill

P11G2007 – Kinetic Energy of a Spool

P11G2008 – Rotating Rod

P11G2016 – Unraveling a String Wound on a Sphere

P11G2017 – Velocity of a Rolling Disk

P11G2018 – Two-Disk Pulley

P11R2015 – Down the Incline

P11G2015 – Around the Loop

P11R2015 – Rolling Without Slipping Around a Loop

P11G2005 – Pulley with Friction

P11Y2016 – Unraveling a String

Spinning Bike Wheel

P11R2015 – Atwood Machine

-- FLUIDS --

Fluids – Lecture

9 Topics

P12-010 – Definitions for Fluids

PNC-12-020 – Mass Density & Pressure

PNC-12-040 – Hydrostatic Pressure Equation

P12-050 – Buoyant Force & Archimedes’ Principle

P12-060 – Floating Condition and Neutrally Buoyant Objects

P12-070 – Pascal’s Principle

P12-090 – Volume Flow Rate & Mass Flow Rate

P12-100 – Continuity Equation

P12-110 – Bernoulli’s Equation

Fluids – Problems

14 Topics

P12G2005 – Floating Glass Beaker

P12G2007 – Boat with a Ballast

P12G2016 – Floating Cylinder

P12G2019 – Anchored Barge

P12R2015 – U-Shaped Tube with Oil and Water

P12R2015 – The Hidden Part of the Iceberg

P12G2018 – Piece of Iron with Cavities

P12G2016 – Flow Through a Horizontal Pipe

P12G2019 – Large Hole in Water Tank

P12G2008 – Hose Draining a Tank

P12G2015 – Flow Through a Pipe

P12G2017 – Flow Through Pitot Tube

P12G2018 – Narrow Pipe on a Tank

P12G2007 – Water Leaking Out of a Tank

MIDTERM 2 - STUDY GUIDE

Lowhorn – 8A 2018 Fall – Midterm 2 – L1

4 Topics

P06L2018 – Spring-Launched Mass

P06L2018 – Plate Pieces

P10L2018 – Moment of Inertia of a Pulley

P11L2018 – Drawbridge

Lowhorn – 8A 2019 Fall – Midterm 2 – L1

3 Topics

P06L2019 – Bullet Velocity

P06L2019 – Colliding Hockey Pucks

P05L2019 – Truck Emergency Ramp

Lowhorn – 8A 2021 Spring – Midterm 2 – L1

4 Topics

P07L2021 – Unknown Planet

P06L2021 – Rock Launcher

P06L2021 – Firework

P10L2021 – Pulley Kinematics

Lowhorn – 8A 2022 Spring – Midterm 2 – L1

4 Topics

P05L2022 – Adding Friction to a Launch Ramp

P05L2022 – From One Spring to Another

P06L2022 – Explosion of a Hockey Puck

P07L2022 – Placing a Satellite on Orbit

-- OSCILLATIONS --

Oscillations – Lecture

18 Topics

P13-010 – Oscillatory Motion

P13-020 – Definitions: period, frequency, and amplitude

P13-030 – Modeling Oscillations Mathematically

P13-060 – Methods to Determine the Phase Constant

P13-040 – Velocity & Acceleration of Oscillations

P13-050 – Maximum Speed and Maximum Acceleration

P13-070 – Review: second-order differential equations

P13-080 – Classic Oscillators: horizontal mass-spring oscillator

P13-090 – Classic Oscillators: vertical mass-spring oscillator

P13-100 – Classic Oscillators: simple pendulum

P13-110 – Classic Oscillators: physical pendulum

P13-120 – Classic Oscillators: torsional pendulum

PNC-13-130 – Conservation of Energy: horizontal oscillator

PNC-13-140 – Conservation of Energy: vertical mass-spring oscillator

PNC-13-150 – Conservation of Energy: simple pendulum

PNC-13-160 – Conservation of Energy: physical pendulum

PNC-13-170 – Conservation of Energy: torsional pendulum

P13-180 – Springs in Series or in Parallel

Oscillations – Problems

11 Topics

P13R2015 – Mathematics of Oscillations

P13R2015 – Springs in Series and in Parallel

P13G2008 – Oscillating Block

P13G2017 – Horizontal Oscillator

P13G2019 – Mass of an Oscillating Block

P13R2015 – Superposed Oscillating Blocks

P13R2015 – Choosing a Torsional Constant

P13G2015 – Collision then Oscillations

P13G2018 – Mass Dropped on an Oscillator

P13R2015 – Energy of a Horizontal Oscillator

P13R2015 – Energy of a Simple Pendulum

-- CALORIMETRY --

Calorimetry – Lecture

7 Topics

P15-010 – Thermal Equilibrium: the zeroth law

P15-020 – Temperature Scales

P15-030 – Thermal Expansion of Solids

P15-040 – Phase Change of a Pure Compound

P15-050 – Heat

P15-060 – Calorimetry

P15-070 – Specific Heat & Latent Heat

Calorimetry – Problems

7 Topics

P15G2018 – Composition of Final Mixture

P15G2017 – Water Vapor and Ice

P15R2015 – Cooling of a Metal Disk

P15R2015 – Heating an Ice Cube

P15R2020 – Whiskey on the Rocks

P15R2009 – Magic Shell

P15B2018 – Heating and Cooling Horseshoe

-- 1st LAW OF THERMODYNAMICS --

First Law – Lecture

10 Topics

P17-010 – Thermodynamic Transformations of a System

P17-020 – PV Diagram & Processes

P17-030 – Internal Energy

P17-040 – First Law of Thermodynamics

PNC-17-050 – Work Done by an Ideal Gas

P17-060 – Heat Transfer for an Ideal Gas

P17-070 – Free Expansion

P17-080 – Thermal Devices

P17-090 – Heat Engine

P17-100 – Efficiency of a Heat Engine

First Law – Problems

15 Topics

P17G2007 – Ideal Gas in a Cylinder

P17R2015 – Final Height of a Piston

P17R2015 – Gas Compression

P17R2015 – Cylinder with Moving Piston

P17G2007 – Work and Heat over a Cycle

P17B2017 – Cyclic Process

P17G2008 – Mystery Process

P17G2016 – Thermodynamic Cycle

P17G2017 – Three-Step Cycle

P17G2018 – Heat Transfer over a Cycle

P17G2019 – Cycle with Linear Segment

P17G2015 – Cycle of a Monatomic Gas

P17B2018 – Heat Engine and Square Cycle

P17L2015 – Solar Energy for Air Conditioning

P17R2015 – Engine or Refrigerator

FINAL EXAM - STUDY GUIDE

Lowhorn – 8A 2018 Fall – Final – L1

4 Topics

P13L2018 – Dropping a Putty Clump on a Scale

P12L2018 – Floating Cubical Block

P02L2018 – Flying Trapeze

P09L2018 – Resting Mountain Climber

Lowhorn – 8A 2019 Fall – Final – L1

4 Topics

P12L2019 – Rock Hanging from an Elevator Ceiling

P05L2019 – Box of Gravel Pulled by a Bucket of Concrete

P06L2019 – Chemical Energy of Fireworks

P09L2019 – Meter Stick with Suspended Block

Lowhorn – 8A 2021 Spring – Final – L1

6 Topics

P17L2021 – Heating and Expansion of an Ideal Gas

P10L2021 – Oscillating Dumbbell

P12L2021 – Gravity on an Unknown Planet

P12L2021 – Pressure in a Draining Pipe

P09L2021 – Angled Suspended Beam

P11L2021 – Momentum of a Sandbag and a Cart

Lowhorn – 8A 2022 – Spring – Final – L1

6 Topics

P13L2022 – Two Oscillating Blocks

P12L2022 – Fluids Questions

P09L2022 – Yoga Pose

P11L2022 – Launching a Rolling Ball

P17L2022 – Heat Engine and Diatomic Gas

P13L2022 – Swinging on a Rope

P02-050 – Property of the Path of the Projectile

Physics 8A – Fall 2023 (Lowhorn) Projectile Motion – Lecture P02-050 – Property of the Path of the Projectile

Property of the path of the projectile:

For a given initial velocity $\overrightarrow{v_0}$ launch angles of ${\theta }_0$ and $90-{\theta }_0$ achieve the same range.

If ${\theta }_0<45{}^\circ $

The projectile then has more horizontal velocity than vertical velocity: it spends little time being airborne but since it travels fast horizontally, it covers the distance $x_M$.

If ${\theta }_0>45{}^\circ $

The projectile then has more vertical velocity than horizontal velocity: it spends more time being airborne which compensates for its low horizontal speed and still allows it to cover the distance $x_M$.