Table of contents
- 0. Math Review(0)
- 1. Intro to Physics Units(0)
- 2. 1D Motion / Kinematics(0)
- Vectors, Scalars, & Displacement(0)
- Average Velocity(0)
- Intro to Acceleration(0)
- Position-Time Graphs & Velocity(0)
- Conceptual Problems with Position-Time Graphs(0)
- Velocity-Time Graphs & Acceleration(0)
- Calculating Displacement from Velocity-Time Graphs(0)
- Conceptual Problems with Velocity-Time Graphs(0)
- Calculating Change in Velocity from Acceleration-Time Graphs(0)
- Graphing Position, Velocity, and Acceleration Graphs(0)
- Kinematics Equations(0)
- Vertical Motion and Free Fall(0)
- Catch/Overtake Problems(0)
- 3. Vectors(0)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(0)
- Adding Vectors Graphically(0)
- Vector Composition & Decomposition(0)
- Adding Vectors by Components(0)
- Trig Review(0)
- Unit Vectors(0)
- Introduction to Dot Product (Scalar Product)(0)
- Calculating Dot Product Using Components(0)
- Intro to Cross Product (Vector Product)(0)
- Calculating Cross Product Using Components(0)
- 4. 2D Kinematics(0)
- 5. Projectile Motion(0)
- 6. Intro to Forces (Dynamics)(0)
- 7. Friction, Inclines, Systems(0)
- 8. Centripetal Forces & Gravitation(0)
- Uniform Circular Motion(0)
- Period and Frequency in Uniform Circular Motion(0)
- Centripetal Forces(0)
- Vertical Centripetal Forces(0)
- Flat Curves(0)
- Banked Curves(0)
- Newton's Law of Gravity(0)
- Gravitational Forces in 2D(0)
- Acceleration Due to Gravity(0)
- Satellite Motion: Intro(0)
- Satellite Motion: Speed & Period(0)
- Geosynchronous Orbits(0)
- Overview of Kepler's Laws(0)
- Kepler's First Law(0)
- Kepler's Third Law(0)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(0)
- Gravitational Potential Energy for Systems of Masses(0)
- Escape Velocity(0)
- Energy of Circular Orbits(0)
- Energy of Elliptical Orbits(0)
- Black Holes(0)
- Gravitational Force Inside the Earth(0)
- Mass Distribution with Calculus(0)
- 9. Work & Energy(0)
- 10. Conservation of Energy(0)
- Intro to Energy Types(0)
- Gravitational Potential Energy(0)
- Intro to Conservation of Energy(0)
- Energy with Non-Conservative Forces(0)
- Springs & Elastic Potential Energy(0)
- Solving Projectile Motion Using Energy(0)
- Motion Along Curved Paths(0)
- Rollercoaster Problems(0)
- Pendulum Problems(0)
- Energy in Connected Objects (Systems)(0)
- Force & Potential Energy(0)
- 11. Momentum & Impulse(0)
- Intro to Momentum(0)
- Intro to Impulse(0)
- Impulse with Variable Forces(0)
- Intro to Conservation of Momentum(0)
- Push-Away Problems(0)
- Types of Collisions(0)
- Completely Inelastic Collisions(0)
- Adding Mass to a Moving System(0)
- Collisions & Motion (Momentum & Energy)(0)
- Ballistic Pendulum(0)
- Collisions with Springs(0)
- Elastic Collisions(0)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(0)
- 12. Rotational Kinematics(0)
- 13. Rotational Inertia & Energy(0)
- More Conservation of Energy Problems(0)
- Conservation of Energy in Rolling Motion(0)
- Parallel Axis Theorem(0)
- Intro to Moment of Inertia(0)
- Moment of Inertia via Integration(0)
- Moment of Inertia of Systems(0)
- Moment of Inertia & Mass Distribution(0)
- Intro to Rotational Kinetic Energy(0)
- Energy of Rolling Motion(0)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(0)
- Torque with Kinematic Equations(0)
- Rotational Dynamics with Two Motions(0)
- Rotational Dynamics of Rolling Motion(0)
- 14. Torque & Rotational Dynamics(0)
- 15. Rotational Equilibrium(0)
- 16. Angular Momentum(0)
- Opening/Closing Arms on Rotating Stool(0)
- Conservation of Angular Momentum(0)
- Angular Momentum & Newton's Second Law(0)
- Intro to Angular Collisions(0)
- Jumping Into/Out of Moving Disc(0)
- Spinning on String of Variable Length(0)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(0)
- Angular Momentum of a Point Mass(0)
- Angular Momentum of Objects in Linear Motion(0)
- 17. Periodic Motion(0)
- 18. Waves & Sound(0)
- Intro to Waves(0)
- Velocity of Transverse Waves(0)
- Velocity of Longitudinal Waves(0)
- Wave Functions(0)
- Phase Constant(0)
- Average Power of Waves on Strings(0)
- Wave Intensity(0)
- Sound Intensity(0)
- Wave Interference(0)
- Superposition of Wave Functions(0)
- Standing Waves(0)
- Standing Wave Functions(0)
- Standing Sound Waves(0)
- Beats(0)
- The Doppler Effect(0)
- 19. Fluid Mechanics(0)
- 20. Heat and Temperature(0)
- Temperature(0)
- Linear Thermal Expansion(0)
- Volume Thermal Expansion(0)
- Moles and Avogadro's Number(0)
- Specific Heat & Temperature Changes(0)
- Latent Heat & Phase Changes(0)
- Intro to Calorimetry(0)
- Calorimetry with Temperature and Phase Changes(0)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(0)
- Phase Diagrams, Triple Points and Critical Points(0)
- Heat Transfer(0)
- 21. Kinetic Theory of Ideal Gases(0)
- 22. The First Law of Thermodynamics(0)
- 23. The Second Law of Thermodynamics(0)
- 24. Electric Force & Field; Gauss' Law(0)
- 25. Electric Potential(0)
- 26. Capacitors & Dielectrics(0)
- 27. Resistors & DC Circuits(0)
- 28. Magnetic Fields and Forces(0)
- 29. Sources of Magnetic Field(0)
- Magnetic Field Produced by Moving Charges(0)
- Magnetic Field Produced by Straight Currents(0)
- Magnetic Force Between Parallel Currents(0)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops andย Solenoids(0)
- Toroidal Solenoids aka Toroids(0)
- Biot-Savart Law (Calculus)(0)
- Ampere's Law (Calculus)(0)
- 30. Induction and Inductance(0)
- 31. Alternating Current(0)
- Alternating Voltages and Currents(0)
- RMS Current and Voltage(0)
- Phasors(0)
- Resistors in AC Circuits(0)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(0)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(0)
- Phasors for Inductors(0)
- Impedance in AC Circuits(0)
- Series LRC Circuits(0)
- Resonance in Series LRC Circuits(0)
- Power in AC Circuits(0)
- 32. Electromagnetic Waves(0)
- 33. Geometric Optics(0)
- 34. Wave Optics(0)
- 35. Special Relativity(0)
16. Angular Momentum
Opening/Closing Arms on Rotating Stool
16. Angular Momentum
Opening/Closing Arms on Rotating Stool: Study with Video Lessons, Practice Problems & Examples
3PRACTICE PROBLEM
A ballet dancer performs pirouettes, rotating at: 1.5, 2.5, and 3.5 revolutions about a vertical axis while she is airborne. The dancer leaps in an "open" position with an initial moment of inertia of ๐ผ0 and a rotational frequency of ๐0 = 1.0 rev/s. When the dancer pulls in their limbs towards their body, the inertia is reduced to ๐ผ and spins at frequency of ๐ before extending their limbs outwards once again before landing back on the ground. What is the change in the angular momentum during the dancer's pirouette? Neglect air resistance.
![Illustration of a ballet dancer performing pirouettes, showing changes in rotational frequency.](data:image/png;base64,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)
A ballet dancer performs pirouettes, rotating at: 1.5, 2.5, and 3.5 revolutions about a vertical axis while she is airborne. The dancer leaps in an "open" position with an initial moment of inertia of ๐ผ0 and a rotational frequency of ๐0 = 1.0 rev/s. When the dancer pulls in their limbs towards their body, the inertia is reduced to ๐ผ and spins at frequency of ๐ before extending their limbs outwards once again before landing back on the ground. What is the change in the angular momentum during the dancer's pirouette? Neglect air resistance.