02.03A · Cours 3 — Rotations

Course 3 — Rotations

1. Physique · 35 pages

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Rotational Kinematics

2Trajectory of a Rotating Object 3Angular Position and Velocity 4Frequency and Period 5Exercise: Carousel Speeding Up

Rotational Acceleration

6Tangential vs Centripetal Acceleration 7Tangential and Angular Acceleration 8Centripetal Acceleration 9Turning and Static Friction 10Exercise: Cutting a Corner 11Cutting the Corner — Larger Radius

Angular Vectors

12Angular Velocity Vector 13Exercise: Right-Hand Rule on Bicycle 14Angular Acceleration Vector 15Exercise: Force to Spin a Wheel

16Opening a Door — Translation vs Rotation 17Torque Definition — τ = r × F 18Exercise: Pedal Torque Direction 19Newton's 2nd Law for Rotation

Moment of Inertia

20Definition — Point and Extended Objects 21Common Shape Formulas

Angular Momentum

22Definition — L = Iω·ω 23Conservation — Rotating Chair Demo 24Conservation — Skater Example

25Gyroscope as Orientation Reference 26Gyroscope Demonstration 27Exercise: Spinning CD in Zero Gravity 28Gyroscope — Continued

Torque Equilibrium Applications

29Pulley — Tension Transmission 30Statics — The Back

31Torque Direction — Parallel vs Perpendicular 32Precession Demonstration 33Precession Rate — Ω ≈ τ/L 34Precession — Intuitive View

35Summary — Translation vs Rotation

02.03APage 1Rotations

Cours 3 — Rotations page 1

02.03APage 2RotationsRotational KinematicsTrajectory of a Rotating Object

Cours 3 — Rotations page 2

02.03APage 3RotationsRotational KinematicsAngular Position and Velocity

Cours 3 — Rotations page 3

02.03APage 4RotationsRotational KinematicsFrequency and Period

Cours 3 — Rotations page 4

02.03APage 5RotationsRotational KinematicsExercise: Carousel Speeding Up

Cours 3 — Rotations page 5

02.03APage 6RotationsRotational AccelerationTangential vs Centripetal Acceleration

Cours 3 — Rotations page 6

02.03APage 7RotationsRotational AccelerationTangential and Angular Acceleration

Cours 3 — Rotations page 7

02.03APage 8RotationsRotational AccelerationCentripetal Acceleration

Cours 3 — Rotations page 8

02.03APage 9RotationsRotational AccelerationTurning and Static Friction

Cours 3 — Rotations page 9

02.03APage 10RotationsRotational AccelerationExercise: Cutting a Corner

Cours 3 — Rotations page 10

02.03APage 11RotationsRotational AccelerationCutting the Corner — Larger Radius

Cours 3 — Rotations page 11

02.03APage 12RotationsAngular VectorsAngular Velocity Vector

Cours 3 — Rotations page 12

02.03APage 13RotationsAngular VectorsExercise: Right-Hand Rule on Bicycle

Cours 3 — Rotations page 13

02.03APage 14RotationsAngular VectorsAngular Acceleration Vector

Cours 3 — Rotations page 14

02.03APage 15RotationsAngular VectorsExercise: Force to Spin a Wheel

Cours 3 — Rotations page 15

02.03APage 16RotationsTorqueOpening a Door — Translation vs Rotation

Cours 3 — Rotations page 16

02.03APage 17RotationsTorqueTorque Definition — τ = r × F

Cours 3 — Rotations page 17

02.03APage 18RotationsTorqueExercise: Pedal Torque Direction

Cours 3 — Rotations page 18

02.03APage 19RotationsTorqueNewton's 2nd Law for Rotation

Cours 3 — Rotations page 19

02.03APage 20RotationsMoment of InertiaDefinition — Point and Extended Objects

Cours 3 — Rotations page 20

02.03APage 21RotationsMoment of InertiaCommon Shape Formulas

Cours 3 — Rotations page 21

02.03APage 22RotationsAngular MomentumDefinition — L = Iω·ω

Cours 3 — Rotations page 22

02.03APage 23RotationsAngular MomentumConservation — Rotating Chair Demo

Cours 3 — Rotations page 23

02.03APage 24RotationsAngular MomentumConservation — Skater Example

Cours 3 — Rotations page 24

02.03APage 25RotationsGyroscopeGyroscope as Orientation Reference

Cours 3 — Rotations page 25

02.03APage 26RotationsGyroscopeGyroscope Demonstration

Cours 3 — Rotations page 26

02.03APage 27RotationsGyroscopeExercise: Spinning CD in Zero Gravity

Cours 3 — Rotations page 27

02.03APage 28RotationsGyroscopeGyroscope — Continued

Cours 3 — Rotations page 28

02.03APage 29RotationsTorque Equilibrium ApplicationsPulley — Tension Transmission

Cours 3 — Rotations page 29

02.03APage 30RotationsTorque Equilibrium ApplicationsStatics — The Back

Cours 3 — Rotations page 30

02.03APage 31RotationsPrecessionTorque Direction — Parallel vs Perpendicular

Cours 3 — Rotations page 31

02.03APage 32RotationsPrecessionPrecession Demonstration

Cours 3 — Rotations page 32

02.03APage 33RotationsPrecessionPrecession Rate — Ω ≈ τ/L

Cours 3 — Rotations page 33

02.03APage 34RotationsPrecessionPrecession — Intuitive View

Cours 3 — Rotations page 34

02.03APage 35RotationsSummary — Translation vs Rotation

Cours 3 — Rotations page 35