Table of contents
- 0. Math Review(43)
- 1. Intro to Physics Units(186)
- 2. 1D Motion / Kinematics(224)
- Vectors, Scalars, & Displacement(32)
- Average Velocity(18)
- Intro to Acceleration(13)
- Position-Time Graphs & Velocity(18)
- Conceptual Problems with Position-Time Graphs(3)
- Velocity-Time Graphs & Acceleration(17)
- Calculating Displacement from Velocity-Time Graphs(3)
- Conceptual Problems with Velocity-Time Graphs(1)
- Calculating Change in Velocity from Acceleration-Time Graphs(1)
- Graphing Position, Velocity, and Acceleration Graphs(9)
- Kinematics Equations(33)
- Vertical Motion and Free Fall(61)
- Catch/Overtake Problems(15)
- 3. Vectors(101)
- Review of Vectors vs. Scalars(0)
- Introduction to Vectors(3)
- Adding Vectors Graphically(6)
- Vector Composition & Decomposition(24)
- Adding Vectors by Components(33)
- Trig Review(1)
- Unit Vectors(15)
- Introduction to Dot Product (Scalar Product)(9)
- Calculating Dot Product Using Components(1)
- Intro to Cross Product (Vector Product)(8)
- Calculating Cross Product Using Components(1)
- 4. 2D Kinematics(57)
- 5. Projectile Motion(68)
- 6. Intro to Forces (Dynamics)(186)
- 7. Friction, Inclines, Systems(103)
- 8. Centripetal Forces & Gravitation(201)
- Uniform Circular Motion(30)
- Period and Frequency in Uniform Circular Motion(6)
- Centripetal Forces(26)
- Vertical Centripetal Forces(13)
- Flat Curves(5)
- Banked Curves(10)
- Newton's Law of Gravity(23)
- Gravitational Forces in 2D(3)
- Acceleration Due to Gravity(18)
- Satellite Motion: Intro(8)
- Satellite Motion: Speed & Period(12)
- Geosynchronous Orbits(2)
- Overview of Kepler's Laws(4)
- Kepler's First Law(4)
- Kepler's Third Law(17)
- Kepler's Third Law for Elliptical Orbits(0)
- Gravitational Potential Energy(5)
- Gravitational Potential Energy for Systems of Masses(1)
- Escape Velocity(4)
- Energy of Circular Orbits(3)
- Energy of Elliptical Orbits(3)
- Black Holes(1)
- Gravitational Force Inside the Earth(1)
- Mass Distribution with Calculus(2)
- 9. Work & Energy(138)
- 10. Conservation of Energy(110)
- Intro to Energy Types(15)
- Gravitational Potential Energy(8)
- Intro to Conservation of Energy(24)
- Energy with Non-Conservative Forces(3)
- Springs & Elastic Potential Energy(24)
- Solving Projectile Motion Using Energy(2)
- Motion Along Curved Paths(6)
- Rollercoaster Problems(0)
- Pendulum Problems(2)
- Energy in Connected Objects (Systems)(2)
- Force & Potential Energy(24)
- 11. Momentum & Impulse(137)
- Intro to Momentum(13)
- Intro to Impulse(8)
- Impulse with Variable Forces(11)
- Intro to Conservation of Momentum(4)
- Push-Away Problems(13)
- Types of Collisions(12)
- Completely Inelastic Collisions(32)
- Adding Mass to a Moving System(4)
- Collisions & Motion (Momentum & Energy)(10)
- Ballistic Pendulum(4)
- Collisions with Springs(6)
- Elastic Collisions(10)
- How to Identify the Type of Collision(0)
- Intro to Center of Mass(10)
- 12. Rotational Kinematics(91)
- 13. Rotational Inertia & Energy(98)
- More Conservation of Energy Problems(4)
- Conservation of Energy in Rolling Motion(18)
- Parallel Axis Theorem(9)
- Intro to Moment of Inertia(12)
- Moment of Inertia via Integration(7)
- Moment of Inertia of Systems(14)
- Moment of Inertia & Mass Distribution(1)
- Intro to Rotational Kinetic Energy(19)
- Energy of Rolling Motion(4)
- Types of Motion & Energy(0)
- Conservation of Energy with Rotation(4)
- Torque with Kinematic Equations(2)
- Rotational Dynamics with Two Motions(1)
- Rotational Dynamics of Rolling Motion(3)
- 14. Torque & Rotational Dynamics(67)
- 15. Rotational Equilibrium(63)
- 16. Angular Momentum(73)
- Opening/Closing Arms on Rotating Stool(4)
- Conservation of Angular Momentum(33)
- Angular Momentum & Newton's Second Law(6)
- Intro to Angular Collisions(10)
- Jumping Into/Out of Moving Disc(3)
- Spinning on String of Variable Length(1)
- Angular Collisions with Linear Motion(0)
- Intro to Angular Momentum(10)
- Angular Momentum of a Point Mass(4)
- Angular Momentum of Objects in Linear Motion(2)
- 17. Periodic Motion(178)
- 18. Waves & Sound(227)
- Intro to Waves(10)
- Velocity of Transverse Waves(11)
- Velocity of Longitudinal Waves(14)
- Wave Functions(20)
- Phase Constant(2)
- Average Power of Waves on Strings(5)
- Wave Intensity(16)
- Sound Intensity(17)
- Wave Interference(30)
- Superposition of Wave Functions(0)
- Standing Waves(35)
- Standing Wave Functions(5)
- Standing Sound Waves(26)
- Beats(14)
- The Doppler Effect(22)
- 19. Fluid Mechanics(170)
- 20. Heat and Temperature(193)
- Temperature(17)
- Linear Thermal Expansion(25)
- Volume Thermal Expansion(17)
- Moles and Avogadro's Number(19)
- Specific Heat & Temperature Changes(30)
- Latent Heat & Phase Changes(9)
- Intro to Calorimetry(10)
- Calorimetry with Temperature and Phase Changes(16)
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes(7)
- Phase Diagrams, Triple Points and Critical Points(5)
- Heat Transfer(38)
- 21. Kinetic Theory of Ideal Gases(183)
- 22. The First Law of Thermodynamics(103)
- 23. The Second Law of Thermodynamics(126)
- 24. Electric Force & Field; Gauss' Law(218)
- 25. Electric Potential(186)
- 26. Capacitors & Dielectrics(115)
- 27. Resistors & DC Circuits(245)
- 28. Magnetic Fields and Forces(98)
- 29. Sources of Magnetic Field(80)
- Magnetic Field Produced by Moving Charges(5)
- Magnetic Field Produced by Straight Currents(21)
- Magnetic Force Between Parallel Currents(6)
- Magnetic Force Between Two Moving Charges(0)
- Magnetic Field Produced by Loops and Solenoids(25)
- Toroidal Solenoids aka Toroids(6)
- Biot-Savart Law (Calculus)(4)
- Ampere's Law (Calculus)(13)
- 30. Induction and Inductance(154)
- 31. Alternating Current(136)
- Alternating Voltages and Currents(5)
- RMS Current and Voltage(13)
- Phasors(3)
- Resistors in AC Circuits(3)
- Phasors for Resistors(0)
- Capacitors in AC Circuits(28)
- Phasors for Capacitors(0)
- Inductors in AC Circuits(16)
- Phasors for Inductors(0)
- Impedance in AC Circuits(12)
- Series LRC Circuits(24)
- Resonance in Series LRC Circuits(13)
- Power in AC Circuits(19)
- 32. Electromagnetic Waves(61)
- 33. Geometric Optics(234)
- 34. Wave Optics(104)
- 35. Special Relativity(245)
12. Rotational Kinematics
Rotational Velocity & Acceleration
12. Rotational Kinematics
Rotational Velocity & Acceleration: Study with Video Lessons, Practice Problems & Examples
23PRACTICE PROBLEM
A ceiling fan starts to accelerate with an angular acceleration α = 6.7t2 - 3.0t from rest. Here, α is given in rads/s2 and time t is in seconds. Derive an expression for the angular displacement Φ as a function of time given that, when t = 0, Φ = 0, ω = 0.
A ceiling fan starts to accelerate with an angular acceleration α = 6.7t2 - 3.0t from rest. Here, α is given in rads/s2 and time t is in seconds. Derive an expression for the angular displacement Φ as a function of time given that, when t = 0, Φ = 0, ω = 0.