-- KINEMATICS --

Kinematics – Lecture

19 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

P01-070 – Instantaneous Velocity

P01-080 – Instantaneous Acceleration

P01-090 – Relationship Between Velocity & Acceleration

P01-100 – Kinematic Equations with Constant Acceleration

P01-110 – Application: Free-Fall

P01-200 – Angular Position & Displacement

P01-210 – Average Angular Velocity

P01-220 – Average Angular Acceleration

P01-230 – Instantaneous Angular Velocity

P01-240 – Instantaneous Angular Acceleration

P01-250 – Relationship Between Angular Speed & Acceleration

P01-260 – Kinematic Equations for Circular Motion

P01-270 – Relating Angular and Linear Quantities

Kinematics – Problems

16 Topics

P01R2015 – Components & Dot Product

P01G2015 – Average Velocity

P01R2015 – Acceleration on an incline

P01R2015 – Vertical Free-fall

P01G2019 – Rocket Launch

P01G2019 – Cars Racing Alongside Each Other

P01R2021 – Physics Rocks

P01B2020 – Trains Approaching

P01R2015 – Catching the Bus

P01R2015 – Highway Patrol

P01G2007 – Balls Colliding in Mid-air

P01G2008 – Passing a Car

P01B2017 – Dropped and Tossed Balls

P01S2016 – Throwing a Rock from a Truck

P01S2019 – Missiles Colliding

P01S2015 – Dropping vs. Throwing

-- 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

15 Topics

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

P02G2020 – Football Toss

P02G2021 – Projectile Launched from Unknown Height

P02S2008 – A Bouncing Superball

P02S2019 – Ball Flying Past a Window

P02S2013 – Throwing a Rock Over a Plateau

P02S2010 – Tennis Ball Launcher and Mobile Target

P02S2016 – Throwing Gum Out an Elevator

-- DYNAMICS --

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

30 Topics

P03G2018 – Blocks Slipping on an Incline

P03R2015 – Hanging Mass

P03R2015 – Keeping a Box at Rest

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

P03G2005 – Holding Up a Block

P03G2015 – Pushing on Three Blocks

P03B2006 – Who is Pulling Who?

P03G2016 – Joint Inclines

P03G2017 – Pulling Three Blocks

P03G2018 – Pulling and Lifting

P03G2020 – Connected Blocks

P03R2015 – Atwood Machine

P03R2015 – Acceleration Constraint

P03R2015 – Pulling Two Connected Boxes

P03G2021 – Minimum Slipping Force

P03G2022 – Pulling Blocks on an Incline

P03S2008 – Three Blocks at Rest

P03S2016 – Two Blocks Compressing a Spring

P03S2013 – Rocket Launch

P03S2009 – Max and Min Angle of an Incline

P03S2016 – Corvette Flying Off a Cliff

P03S2016 – Pulling Stacked Blocks

P03S2019 – Sliding Up a Wedge at Rest

P03S2008 – Two Blocks on the Verge of Slipping

P03S2013 – Lifting a Box with Pulleys

P03S2015 – Climbing Up a Rope

-- CIRCULAR MOTION --

Circular Motion – Lecture

14 Topics

P04-010 – Circular Motion

P04-020 – RTZ Coordinate System

P04-030 – Direction of Acceleration

P04-040 – Components of Acceleration

P04-050 – Derivation of the 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

P04-100 – Instantaneous Angular Velocity

P04-110 – Instantaneous Angular Acceleration

P04-120 – Relationship Between Velocity and Acceleration

P04-130 – Kinematic Equations for Circular Motion

P04-140 – Relating Angular & Linear Quantities

Circular Motion – Problems

17 Topics

P04G2016 – Lift Force on a Plane

P04B2017 – Interconnected Masses

P04B2020 – Tether Ball

P04B2006 – Space Ride

P04G2017 – Toy Car

P04G2018 – Holding a Block against a Wall

P04S2016 – Sliding Around a Funnel

P04S2016 – Pendulum on Planet Vulcan

P04B2016 – Banked Curve vs. Flat Curve

P04G2019 – Semicircular Hill and Valley

P04G2005 – Flying in a Loop

P04R2015 – Around the Loop

P04G2022 – Pendulum

P04S2016 – Car Driving Inside a Cone

P04S2019 – RC Car in a Can

P04S2013 – Riding Inside a Spherical Cage

P04S2015 – Racing Outside a Banked Curve

-- WORK & ENERGY --

Work & Energy – Lecture

14 Topics

P05-010 – Energy

P05-020 – Kinetic Energy

P05-030 – Gravitational Potential Energy

P05-040 – Elastic Potential Energy

P05-050 – Mechanical Energy

P05-060 – Work Done by a Force

P05-070 – Calculating the Work Done by a Force

P05-080 – Conservative Force

P05-100 – Work Done by the Weight Force

P05-110 – Work Done by the Spring Force

P05-120 – Work-Kinetic Energy Theorem

P05-130 – Derivation of the Work-Kinetic Energy Theorem

P05-140 – Conservation of Mechanical Energy

P05-150 – Power and Mechanical Power

Work & Energy – Problems

20 Topics

P05G2007 – Package Landing on a Spring

P05S2016 – Sliding Over a Hill

P05L2022 – From One Spring to Another

P05G2019 – Block on a Vertical Spring

P05G2020 – Frictionless Ramp

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

P05G2016 – Non-Conservative Force

P05G2018 – Projectile Launched from a Ramp

P05G2019 – Pushing a Block on the Ceiling

P05B2016 – Roller Coaster

P05G2021 – Friction Under a Spring

P05S2009 – Sliding Mounds and Block

P05S2016 – Sliding Down and Bouncing Back Up

P05S2019 – Down and Up Twice

P05S2013 – Stretching a Spring

P05S2015 – Sliding Off a Ramp with Friction

-- IMPULSE & MOMENTUM --

Impulse & Moment. – Lecture

10 Topics

P06-010 – Momentum Vector

P06-020 – Newton’s Second Law in Momentum Form

P06-030 – Conservation of Momentum

P06-040 – Impulse of a Force

P06-050 – How to Calculate an Impulse

P06-060 – 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

20 Topics

P06G2005 – Game of Catch

P06L2018 – Plate Pieces

P06R2015 – Explosion of a Hockey Puck

P06R2015 – Ballistic Pendulum

P06G2019 – Blocks & Compressed Spring

P06B2006 – Saving Lois?

P06G2007 – Three Colliding Blocks

P06G2017 – Sequence of Collisions

P06R2019 – Two Collisions in a Row

P06B2016 – Fireworks

P06G2016 – Collision Between Three Masses

P06G2018 – Masses Bouncing Off Each Other

P06G2020 – Speed Before and After a Collision

P06R2020 – Inelastic Collision vs. Elastic Collision

P06D2009 – Fun with a Slingshot

P06S2008 – Canoe Disagreement

P06S2019 – Space Chase

P06S2013 – Launching Two Blocks with a Spring

P06S2016 – Sliding Blocks Compressing a Spring

P06S2016 – Sliding Down and Back Up

-- CENTER OF MASS --

Center of Mass – Lecture

11 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

P08-060 – Center of Mass of a Rigid Body

P08-070 – Computation: center of mass of a uniform rod of mass

P08-080 – Computation: center of mass of a uniform cylinder

P08-090 – Computation: center of mass of a uniform solid sphere

P08-100 – Computation: center of mass of a compound body

P08-110 – Computation: center of mass of a hollow body

Center of Mass – Problems

11 Topics

P08G2019 – Stacked Blocks

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

P08R2015 – Exploding Firework

P08S2015 – Jumping the Plank

P08R2015 – A Grenade Exploding in Midair

P08R2015 – COM of rigid bodies

-- TORQUE - 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

17 Topics

P09R2020 – Balanced Beam

P09R2020 – Balanced Beam with Hanging Mass

P09B2021 – Drawbridge

P09R2015 – Resting Ladder

P09R2015 – Ladder and Painter

P09B2019 – A Ball Attached to an Incline

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

P09G2020 – Beam with Two Sections

P09S2009 – Disk Balanced Between Rods

P09B2018 – Static Equilibrium of a Crane

P09G2018 – Balanced Pole

-- TORQUE - DYNAMICS --

Dynamics – Lecture

10 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

P10-060 – Computation: moment of inertia of a solid rod

P10-070 – Computation: moment of inertia of a solid cylinder

P10-080 – Computation: moment of inertia of a solid sphere

P10-090 – Parallel-Axis Theorem

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

Dynamics – Problems

19 Topics

P10S2015 – Helicopter Blade

P10G2005 – Rotating a Disk and a Rod

P10G2016 – Rotating Cylinder

P10D2013 – Pushing a Dresser

P10G2018 – Pushing a Door and a Box

P10R2015 – Kinematics of a Hollow Sphere

P10R2015 – Atwood Machine

P10G2019 – Blocks & Non-ideal Pulley

P10G2007 – Pulley Lowering a Block

P10L2018 – Moment of Inertia of a Pulley

P10B2017 – Measuring Rotational Inertia

P10S2016 – Rolling on a Circular Track

P10S2016 – Rolling and Slipping

P10S2009 – Pulling a Spool of Thread

P10S2013 – Pulling Strings Off a Disk

P10S2015 – Spherical Spintop

P10S2019 – Accelerating Joint Disks

P10S2015 – Disk and Mass Contraption

P10S2016 – Block Pulling a Rolling Disk

-- TORQUE - ENERGY & MOMENTUM --

Energy & Moment. – Lecture

11 Topics

P11-010 – Angular Momentum

P11-020 – Newton’s Second Law in Angular Momentum Form

P11-030 – Conservation of Angular Momentum

P11-040 – Impulse-Momentum Theorem of 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

P11-090 – Work Done by a Torque

P11-100 – Work-Kinetic Energy Theorem

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

Energy & Moment. – Problems

17 Topics

P11G2019 – Biking Down a Hill

P11B2012 – Rolling up an Incline

P11G2007 – Kinetic Energy of a Spool

P11G2008 – Rotating Rod

P11G2016 – Unraveling a String Wound on a Sphere

P11G2017 – Velocity of a Rolling Disk

P11R2015 – Atwood Machine

P11G2018 – Two-Disk Pulley

P11R2015 – Down the Incline

P11G2015 – Around the Loop

P11G2005 – Pulley with Friction

P11R2015 – Vertical Swinging Rod

P11S2013 – Rolling Up and Off a Ramp

P11S2015 – Rolling…or Not

P11S2009 – Spring-Launched Objects

P11S2019 – Rolling on a Sliding Plank

P11S2016 – Fleas Jumping Off a Disk

-- FLUIDS --

Fluids – Lecture

10 Topics

P12-010 – Definitions for Fluids

P12-020 – Mass Density & Pressure

P12-030 – Fundamental Equation of Hydrostatics

P12-040 – Hydrostatic Pressure in a Uniform Gravitational Field

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

21 Topics

P12R2015 – U-Shaped Tube with Oil and Water

P12R2015 – The Hidden Part of the Iceberg

P12B2017 – Floating in Two Fluids

P12B2021 – Hydraulic Press

P12G2005 – Floating Glass Beaker

P12G2007 – Boat with a Ballast

P12G2016 – Floating Cylinder

P12G2019 – Anchored Barge

P12G2018 – Piece of Iron with Cavities

P12G2020 – Weighing Suspended Blocks in Water

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

P12R2015 – Pitot Tube

P12G2007 – Water Leaking Out of a Tank

P12S2019 – Suspended Floating Iron Cylinder

P12S2013 – Syringe of Water

P12S2009 – Leaky Cylindrical Tank

-- OSCILLATIONS --

Oscillations – Lecture

19 Topics

P13-010 – Oscillatory Motion

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

P13-030 – Modeling Oscillations Mathematically

P13-040 – Velocity & Acceleration of Oscillations

P13-050 – Maximum Speed and Maximum Acceleration

P13-060 – Methods to Determine the Phase Constant

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

P13-130 – Conservation of Energy: horizontal oscillator

P13-140 – Conservation of Energy: vertical mass-spring oscillator

P13-150 – Conservation of Energy: simple pendulum

P13-160 – Conservation of Energy: physical pendulum

P13-170 – Conservation of Energy: torsional pendulum

P13-180 – Springs in Series or in Parallel

P13-190 – Modeling Damped Oscillations

Oscillations – Problems

16 Topics

P13R2015 – Mathematics of Oscillations

P13R2015 – Energy of a Horizontal Oscillator

P13G2015 – Collision then Oscillations

P13R2015 – Energy of a Simple Pendulum

P13B2017 – Mass-Spring Systems

P13G2008 – Oscillating Block

P13G2017 – Horizontal Oscillator

P13G2019 – Mass of an Oscillating Block

P13R2015 – Superposed Oscillating Blocks

P13G2018 – Mass Dropped on an Oscillator

P13R2015 – Springs in Series and in Parallel

P13S2011 – Oscillating Plate

P13S2013 – Oscillating Rod

P13S2019 – Oscillating While Rolling Without Slipping

P13S2016 – Collision with a Rod

P13S2009 – Elastic Collisions and Oscillations

-- MECHANICAL WAVES --

Mechanical Waves – Lecture

21 Topics

P14-010 – Fundamental Definitions

P14-020 – Classification of Waves

P14-030 – One-Dimensional Sinusoidal Traveling Waves

P14-040 – Period and Wavelength

P14-050 – Speed of a Traveling Wave

P14-060 – Principle of Superposition

P14-070 – Constructive and Destructive Interference

P14-080 – Conditions for Constructive and Destructive Interference

P14-090 – Waves on a String Under Tension

P14-100 – Celerity of a Wave on a String

P14-110 – Reflection of a Wave at a Boundary

P14-120 – Standing Waves

P14-130 – Patterns, Fundamental Frequency, Harmonics

P14-140 – Soundwaves

P14-160 – Standing Waves in a Column of Air

P14-170 – Column of Air Closed at Both Ends

P14-180 – Column of Air Open at Both Ends

P14-190 – Column of Air with Open/Closed Ends

P14-200 – Beats

P14-210 – Doppler Effect

P14-220 – Intensity and Sound Level

Mechanical Waves – Problems

16 Topics

P14G2007 – Standing Wave on a Wire

P14G2015 – Standing Wave on a String

P14G2016 – Vibrating Wire

P14G2018 – Standing Wave Pattern

P14R2015 – Two Strings

P14G2008 – Another Vibrating Wire

P14G2019 – Standing Waves in a Pipe

P14R2015 – A Tuning Fork and a Tube

P14R2015 – Interfering Soundwaves

P14G2007 – Bat Flying Toward a Wall

P14G2015 – Extraterrestrial Doppler Shift

P14G2017 – Doppler-Shifted Train Whistle

P14R2015 – Foghorns on the Bay

P14G2016 – Oscillating Speaker

P14S2009 – Vibrating Hanging Wires

P14Y2010 – Hanging Rope

P02-050 – Property of the Path of the Projectile

Physics 7A – Fall 2024 (Golightly) 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 $x_M$.