-- 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

8A – Kinematics Summary

Kinematics – Problems

21 Topics

P01R2015 – Components & Dot Product

P01R2015 – Graphical Subtraction of Vectors

P01G2015 – Average Velocity

P01L2022 – Kitty Kinematics

P01R2015 – Trip to the Store

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

P01D2017 – Relay Race

P01G2008 – Passing a Car

P01R2015 – Furiously Fast

P01S2015 – Dropping vs. Throwing

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

8A – Projectile Motion Summary

Projectile Motion – Problems

23 Topics

P02R2017 – Hats Off to Frosty

P02G2021 – Projectile Launched from Unknown Height

P02L2018 – Snowball Rolling Off a Roof

P02L2018 – Flying Trapeze

P02L2019 – Slanted Rocket Launch

P02R2015 – Analysis of a Jump

P02R2015 – Hoop Spacing

P02R2015 – Air Delivery

P02G2018 – Air Drop

P02L2021 – Lunch Throw

P02L2022 – Launching a Box Over a Ravine

P02R2015 – A Ball Game

P02S2008 – A Bouncing Superball

P02R2015 – Throwing a Rock Off a Cliff

P02S2019 – Ball Flying Past a Window

P02G2017 – Ball Toss

P02R2015 – Clearing the Edge of a Cliff

P02G2005 – Home Run

P02G2016 – Ball Thrown in the Air

P02G2020 – Football Toss

P02S2013 – Throwing a Rock Over a Plateau

P02S2010 – Tennis Ball Launcher and Mobile Target

P02S2016 – Throwing Gum Out an Elevator

-- 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

8A – Newton’s Laws Summary

Newton’s Laws – Problems

41 Topics

P03R2015 – Three Hanging Masses

P03G2018 – Blocks Slipping on an Incline

P03R2015 – Hanging Mass

P03S2008 – Three Blocks at Rest

P03S2016 – Two Blocks Compressing a Spring

P03R2015 – Keeping a Box at Rest

P03S2013 – Rocket Launch

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

P03L2021 – Crate in a Truck Bed

P03R2015 – Resting or Sliding Up an Incline

P03R2015 – Acceleration and Friction Forces

P03S2009 – Max and Min Angle of an Incline

P03S2016 – Corvette Flying Off a Cliff

P03G2005 – Holding Up a Block

P03G2015 – Pushing on Three Blocks

P03L2018 – Sliding from Under a Plank

P03R2015 – Small Block on Larger Moving Block

P03S2016 – Pulling Stacked Blocks

P03R2015 – Blocks Sliding Down a Ramp

P03S2015 – Small Block Sliding on Another

P03S2019 – Stacked Triangular Blocks

P03S2019 – Sliding Up a Wedge at Rest

P03B2006 – Who is Pulling Who?

P03G2016 – Joint Inclines

P03G2017 – Pulling Three Blocks

P03G2018 – Pulling and Lifting

P03G2020 – Connected Blocks

P03G2021 – Minimum Slipping Force

P03G2022 – Pulling Blocks on an Incline

P03L2019 – Sliding Connected Blocks

P03L2022 – Unknown Suspended Mass

P03R2015 – Atwood Machine

P03R2015 – Acceleration Constraint

P03S2008 – Two Blocks on the Verge of Slipping

P03S2013 – Lifting a Box with Pulleys

P03S2015 – Climbing Up a Rope

P03L2021 – Stacked Blocks and a Pulley

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

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

8A – Circular Motion Summary

Circular Motion – Problems

25 Topics

P04G2016 – Lift Force on a Plane

P04B2006 – Space Ride

P04G2017 – Toy Car

P04G2018 – Holding a Block against a Wall

P04G2022 – Pendulum

P04L2019 – Rotating Block with Two Strings

P04L2021 – Bead on a Rotating Ring

P04R2015 – Connected Blocks and Circular Motion

P04R2017 – Rotating Around a Rod

P04R2019 – Twirling Pendulum

P04S2016 – Car Driving Inside a Cone

P04S2016 – Sliding Around a Funnel

P04S2019 – RC Car in a Can

P04S2016 – Pendulum on Planet Vulcan

P04S2013 – Riding Inside a Spherical Cage

P04L2018 – Banked Curve

P04R2015 – Banked Road

P04S2015 – Racing Outside a Banked Curve

P04D2010 – Ferris Wheel

P04L2022 – Circular Hills and Valleys

P04G2019 – Semicircular Hill and Valley

P04S2015 – Whirling a Stone

P04G2005 – Flying in a Loop

P04R2015 – Around the Loop

P04R2015 – Skateboarding in the Hills

-- 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

8A – Work & Energy Summary

Work & Energy – Problems

30 Topics

P05G2007 – Package Landing on a Spring

P05R2015 – Over Two Hills

P05R2015 – Sliding Down the Track

P05R2015 – Landing on a Spring

P05R2015 – Sliding Down Onto a Spring

P05G2005 – Blocks Connected Over a Pulley

P05L2022 – From One Spring to Another

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

P05L2019 – Box of Gravel Pulled by a Bucket of Concrete

P05R2015 – Springs and Friction

P05R2021 – Launching a Block Up a Rough Incline

P05S2016 – Sliding Down and Bouncing Back Up

P05S2015 – Sliding Across a Track

P05G2016 – Non-Conservative Force

P05G2021 – Friction Under a Spring

P05L2019 – Truck Emergency Ramp

P05L2022 – Adding Friction to a Launch Ramp

P05S2019 – Down and Up Twice

P05G2018 – Projectile Launched from a Ramp

P05G2019 – Pushing a Block on the Ceiling

P05R2015 – Risky Swinging

P05S2013 – Stretching a Spring

P05S2015 – Sliding Off a Ramp with Friction

P05R2015 – Energy of Connected Masses

P05R2015 – Spring, Pulley, and Masses

MIDTERM 1 - STUDY GUIDE

Bordel – 8A 2016 Spring – Midterm 1 – L1

4 Topics

P01B2016 – Jetliner Landing

P02B2016 – Rescue Operation

P04B2016 – Banked Curve vs. Flat Curve

P05B2016 – Swinging on a Vine

Bordel – 8A 2017 Spring – Midterm 1 – L1

4 Topics

P01B2017 – Airport Connection

P04B2017 – Ball Launched from a Tube

P03B2017 – Alpinists in Danger

P05B2017 – Up the Incline

Bordel – 8A 2017 Spring – Midterm 1 – L2

4 Topics

P01B2017 – Dropped and Tossed Balls

P02B2017 – Golf Course

P04B2017 – Interconnected Masses

P05B2017 – Loop the Loop

Bordel – 8A 2018 Spring – Midterm 1 – L1

4 Topics

P01B2018 – Tiger on a Linear Hunting Path

P02B2018 – The Impressive Spit of the Archerfish

P03B2018 – Baby Bouncer

P04B2018 – Car Rounding a Curve

Bordel – 8A 2018 Fall – Midterm 1 – L2

4 Topics

P01B2018 – The Tortoise & the Hare

P02B2018 – Stranded on a Desert Island

P03B2018 – Pushing a Crate

P04B2018 – Interconnected Blocks

Bordel – 8A 2019 Fall – Midterm 1 – L2

4 Topics

P01B2019 – Stop-and-Go Traffic

P02B2019 – Water Balloon Game

P03B2019 – Water Skiing

P04B2019 – A Fairground Ride

Bordel – 8A 2020 Spring – Midterm 1 – L1

4 Topics

P01B2020 – Miniature Rocket Launch

P02B2020 – Medieval Attack Reenactment

P03B2020 – Sliding Blocks

P04B2020 – A Fun Ride

Bordel – 8A 2020 Fall – Midterm 1 – L2

4 Topics

P01B2020 – Trains Approaching

P02B2020 – Ball Thrower

P03B2020 – Blocks and Pulley

P04B2020 – Tether Ball

Bordel – 8A 2021 Spring – Midterm 1 – L2

4 Topics

P01B2021 – Brake Failure

P02B2021 – Ring Toss

P05B2021 – Ski Patrol

P04B2021 – Racing Outside of a Cone

Bordel – 8A 2023 Spring – Midterm 1 – L1

4 Topics

P02B2023 – Jump of a Grasshopper

P05B2023 – Ski Lift

P04B2023 – Cube on a Rotating Disk

P05B2023 – Boat Launch Ramp

Bordel – 8A 2024 Spring – Midterm 1 – L1

4 Topics

P02R2024 – Ball Landing on an Incline

P05B2024 – Ski Patrol

P04B2024 – Interconnected Blocks

P05B2024 – Up the Incline

8A Masterclass – Practice Midterm 1 (graded)

8A Masterclass – Midterm 1 Review Session

-- GRAVITATION --

Gravitation – Lecture

16 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

P07-100 – 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

8A – Gravitation Summary

Gravitation – Problems

10 Topics

P07R2015 – Accelerations Due to Gravity

P07S2015 – Mass Density of the Earth & the Moon

P07R2015 – Orbiting Satellite

P07R2015 – Geostationary Satellite

P07S2013 – Three Orbiting Bodies

P07S2013 – Orbiting the Center of Mass

P07L2021 – Unknown Planet

P07L2022 – Placing a Satellite on Orbit

P07R2015 – Satellite Orbiting Earth

P07R2015 – Of Kepler’s Laws

-- 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

8A – Impulse & Momentum Summary

Impulse & Moment. – Problems

21 Topics

P06G2005 – Game of Catch

P06R2015 – Ball Bouncing Off a Wall

P06R2015 – Hockey Puck Bouncing Off a Wall

P06R2019 – Bullet Fired into a Block

P06S2019 – Space Chase

P06G2019 – Blocks & Compressed Spring

P06B2006 – Saving Lois?

P06G2007 – Three Colliding Blocks

P06G2017 – Sequence of Collisions

P06R2017 – Collision Course

P06R2019 – Two Collisions in a Row

P06S2013 – Launching Two Blocks with a Spring

P06S2016 – Sliding Blocks Compressing a Spring

P06G2015 – Inelastic Collision

P06G2016 – Collision Between Three Masses

P06G2018 – Masses Bouncing Off Each Other

P06G2020 – Speed Before and After a Collision

P06R2015 – Blocks Colliding

P06R2015 – Explosion of a Hockey Puck

P06R2020 – Inelastic Collision vs. Elastic Collision

P06S2016 – Sliding Down and Back Up

-- 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

8A – Statics Summary

Statics – Problems

18 Topics

P09G2018 – Balanced Pole

P09R2015 – Ladder and Painter

P09R2015 – Resting Ladder

P09R2020 – Balanced Beam

P09S2016 – Balanced Sphere

P09S2016 – Disk Balanced on an Incline

P09R2015 – Straw Balanced Across a Glass

P09S2009 – Disk Balanced Between Rods

P09G2019 – Non-Uniform Hanging Bar

P09R2015 – Non-Uniform Balancing Rod

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

P09L2022 – Yoga Pose

P09R2021 – Balancing Force

-- TORQUE - 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

8A – Dynamics Summary

Dynamics – Problems

22 Topics

P10G2005 – Rotating a Disk and a Rod

P10G2016 – Rotating Cylinder

P10R2020 – Rotating a Disk

P10G2018 – Pushing a Door and a Box

P10R2015 – Kinematics of a Hollow Sphere

P10R2015 – Two Rockets on a Rod

P10S2016 – Rolling on a Circular Track

P10S2016 – Rolling and Slipping

P10S2015 – Helicopter Blade

P10S2009 – Pulling a Spool of Thread

P10S2013 – Pulling Strings Off a Disk

P10S2015 – Spherical Spintop

P10S2019 – Accelerating Joint Disks

P10G2019 – Blocks & Non-ideal Pulley

P10G2007 – Pulley Lowering a Block

P10G2015 – Acceleration of a Pulley

P10R2015 – Atwood Machine

P10R2015 – A Non-Ideal Pulley

P10R2017 – Cylinder Dragging a Box

P10R2020 – Pulley Lowering a Block

P10S2015 – Disk and Mass Contraption

P10S2016 – Block Pulling a Rolling Disk

-- TORQUE - ENERGY & MOMENTUM --

Energy & Moment. – Lecture

10 Topics

P11-010 – Angular Momentum

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

P11-030 – Conservation 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

8A – Energy & Momentum Summary

Energy & Moment. – Problems

26 Topics

P11G2019 – Biking Down a Hill

P11G2007 – Kinetic Energy of a Spool

P11G2008 – Rotating Rod

P11G2015 – Disk Rolling then Sliding

P11G2016 – Unraveling a String Wound on a Sphere

P11G2017 – Velocity of a Rolling Disk

P11G2018 – Two-Disk Pulley

P11R2015 – Down the Incline

P11S2013 – Rolling Up and Off a Ramp

P11S2015 – Rolling…or Not

P11G2015 – Around the Loop

P11R2015 – Rolling Without Slipping Around a Loop

P11S2009 – Spring-Launched Objects

P11D2014 – Bar Suspended by a Rope

P11D2017 – Swinging Bar

P11G2005 – Pulley with Friction

P11R2015 – Vertical Swinging Rod

P11B2006 – Rusty Barn Door

P11L2021 – Momentum of a Sandbag and a Cart

P11S2016 – Fleas Jumping Off a Disk

P11G2015 – Collision with a Swinging Stick

P11S2013 – All Sorts of Momentum

P11R2015 – Atwood Machine

P11R2015 – Jumping on a Carousel

P11D2015 – Throwing a Rubber Ball at a Sign

P11S2019 – Stopping a Rotating Rod

MIDTERM 2 - STUDY GUIDE

Bordel – 8A 2012 Spring – Midterm 2 – L2

4 Topics

P07B2012 – Orbiting Spaceship

P06B2012 – Cars Colliding

P11B2012 – Rolling up an Incline

P09B2012 – Car Rescue

Bordel – 8A 2016 Spring – Midterm 2 – L2

4 Topics

P07B2016 – Space Maneuvers

P05B2016 – Roller Coaster

P06B2016 – Fireworks

P11B2016 – Potter Wheel

Bordel – 8A 2017 Spring – Midterm 2 – L1

4 Topics

P07B2017 – Blast Off

P05B2017 – Sliding Block

P06B2017 – Ballistic Pendulum

P11B2017 – Throwing Mud

Bordel – 8A 2017 Spring – Midterm 2 – L2

4 Topics

P07B2017 – Satellite and Asteroid

P05B2017 – Ball Launcher

P06B2017 – Fun at the Arcade

P11B2017 – Spinning Wheel

Bordel – 8A 2018 Spring – Midterm 2 – L1

4 Topics

P05B2018 – Loop-the-Loop

P06B2018 – Colliding Particles

P10B2018 – Block Lowered by a Pulley

P11B2018 – A Playful Mouse

Bordel – 8A 2018 Fall – Midterm 2 – L2

4 Topics

P05B2018 – Puck on an Incline

P06B2018 – Collision with a Pendulum

P10B2018 – Dropping Anchor

P11B2018 – Ball Race

Bordel – 8A 2019 Fall – Midterm 2 – L2

4 Topics

P07B2019 – Mars & Jupiter

P05B2019 – Santa Claus Contest

P06B2019 – Lodging a Bead in a Block

P10B2019 – Dropping the Bucket into the Well

1 of 2

P01R2015 – Biking Along

8A Masterclass (Bordel) Kinematics – Problems P01R2015 – Biking Along

Biking Along

Two bicyclists, A and B, are on a straight road. Biker A, initially at rest, starts accelerating with constant acceleration $a_A=1\ m/s^2$ at $t=0$ until she reaches a speed $v=5\ m/s$. She then cruises at constant speed $v=5\ m/s$. Biker B is initially moving at $12\ m/s$ and is $10\ m$ ahead of biker A. At $t=0$, biker B begins to brake and slows down to a stop with a constant deceleration $a_B=-2\ m/s^2$.

Using graphs only,

1. Determine the distance traveled by biker A when she reaches a speed $v=5\ m/s$.

View answer

We start by graphing the velocity of biker A and biker B on the graph below:

Biker A reaches a speed of $1\ m/s$ at time $t=5\ s$ and the distance $d_A$ she traveled in that time is equal to the area under the (red) curve $v_A\left(t\right)$ between $t=0$ and $t=5$.

Thus,we conclude that when she reaches a speed $v=5\ m/s$, biker A will have traveled a distance equal to

\boxed{d_A=\frac{5\cdot 5}{2}=12.5\ m}

2. Find when both bikers have the same velocity. What distance has biker B traveled in that time?

View answer

Both bikers have the same velocity when the two curves intersect i.e. when $t=4\ s$.

3. Find how long it takes biker B to stop.

View answer

Biker B stops when its velocity is equal to zero which occurs at $t=6\ s$.

4. Derive what the acceleration $a_B$ of biker B must be equal to for both bikers to a reach a speed of $5\ m/s$ at the same time.

View answer

For the bikers to reach a speed of $5\ m/s$ at the same time, the velocities curves must intersect at point $\left(5,5\right)$ as shown in the graph below:

The acceleration of biker B is given by the slope of the new curve which goes through points $\left(0,12\right)$ and $\left(5,5\right)$. The new acceleration of biker B which allows him to reach a speed of $5\ m/s$ at the same time as biker A is equal to

\boxed{a_B=\frac{12-5}{0-5}=-\frac{7}{5}=-1.4\ m/s^2}