Multiple Choice
A 150-g baseball, 3.85 cm in radius, leaves the pitcher's hand with 30 m/s horizontal and 20 rad/s clockwise. Calculate the ball's linear, rotational, and total kinetic energy.
Table of contents
- 0. Math Review
- 1. Intro to Physics Units
- 2. 1D Motion / Kinematics
- Vectors, Scalars, & Displacement
- Average Velocity
- Intro to Acceleration
- Position-Time Graphs & Velocity
- Conceptual Problems with Position-Time Graphs
- Velocity-Time Graphs & Acceleration
- Calculating Displacement from Velocity-Time Graphs
- Conceptual Problems with Velocity-Time Graphs
- Calculating Change in Velocity from Acceleration-Time Graphs
- Graphing Position, Velocity, and Acceleration Graphs
- Kinematics Equations
- Vertical Motion and Free Fall
- Catch/Overtake Problems
- 3. Vectors
- Review of Vectors vs. Scalars
- Introduction to Vectors
- Adding Vectors Graphically
- Vector Composition & Decomposition
- Adding Vectors by Components
- Trig Review
- Unit Vectors
- Introduction to Dot Product (Scalar Product)
- Calculating Dot Product Using Components
- Intro to Cross Product (Vector Product)
- Calculating Cross Product Using Components
- 4. 2D Kinematics
- 5. Projectile Motion
- 6. Intro to Forces (Dynamics)
- 7. Friction, Inclines, Systems
- 8. Centripetal Forces & Gravitation
- Uniform Circular Motion
- Period and Frequency in Uniform Circular Motion
- Centripetal Forces
- Vertical Centripetal Forces
- Flat Curves
- Banked Curves
- Newton's Law of Gravity
- Gravitational Forces in 2D
- Acceleration Due to Gravity
- Satellite Motion: Intro
- Satellite Motion: Speed & Period
- Geosynchronous Orbits
- Overview of Kepler's Laws
- Kepler's First Law
- Kepler's Third Law
- Kepler's Third Law for Elliptical Orbits
- Gravitational Potential Energy
- Gravitational Potential Energy for Systems of Masses
- Escape Velocity
- Energy of Circular Orbits
- Energy of Elliptical Orbits
- Black Holes
- Gravitational Force Inside the Earth
- Mass Distribution with Calculus
- 9. Work & Energy
- 10. Conservation of Energy
- Intro to Energy Types
- Gravitational Potential Energy
- Intro to Conservation of Energy
- Energy with Non-Conservative Forces
- Springs & Elastic Potential Energy
- Solving Projectile Motion Using Energy
- Motion Along Curved Paths
- Rollercoaster Problems
- Pendulum Problems
- Energy in Connected Objects (Systems)
- Force & Potential Energy
- 11. Momentum & Impulse
- Intro to Momentum
- Intro to Impulse
- Impulse with Variable Forces
- Intro to Conservation of Momentum
- Push-Away Problems
- Types of Collisions
- Completely Inelastic Collisions
- Adding Mass to a Moving System
- Collisions & Motion (Momentum & Energy)
- Ballistic Pendulum
- Collisions with Springs
- Elastic Collisions
- How to Identify the Type of Collision
- Intro to Center of Mass
- 12. Rotational Kinematics
- 13. Rotational Inertia & Energy
- More Conservation of Energy Problems
- Conservation of Energy in Rolling Motion
- Parallel Axis Theorem
- Intro to Moment of Inertia
- Moment of Inertia via Integration
- Moment of Inertia of Systems
- Moment of Inertia & Mass Distribution
- Intro to Rotational Kinetic Energy
- Energy of Rolling Motion
- Types of Motion & Energy
- Conservation of Energy with Rotation
- Torque with Kinematic Equations
- Rotational Dynamics with Two Motions
- Rotational Dynamics of Rolling Motion
- 14. Torque & Rotational Dynamics
- 15. Rotational Equilibrium
- 16. Angular Momentum
- Opening/Closing Arms on Rotating Stool
- Conservation of Angular Momentum
- Angular Momentum & Newton's Second Law
- Intro to Angular Collisions
- Jumping Into/Out of Moving Disc
- Spinning on String of Variable Length
- Angular Collisions with Linear Motion
- Intro to Angular Momentum
- Angular Momentum of a Point Mass
- Angular Momentum of Objects in Linear Motion
- 17. Periodic Motion
- 18. Waves & Sound
- 19. Fluid Mechanics
- 20. Heat and Temperature
- Temperature
- Linear Thermal Expansion
- Volume Thermal Expansion
- Moles and Avogadro's Number
- Specific Heat & Temperature Changes
- Latent Heat & Phase Changes
- Intro to Calorimetry
- Calorimetry with Temperature and Phase Changes
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes
- Phase Diagrams, Triple Points and Critical Points
- Heat Transfer
- 21. Kinetic Theory of Ideal Gases
- 22. The First Law of Thermodynamics
- 23. The Second Law of Thermodynamics
- 24. Electric Force & Field; Gauss' Law
- 25. Electric Potential
- 26. Capacitors & Dielectrics
- 27. Resistors & DC Circuits
- 28. Magnetic Fields and Forces
- 29. Sources of Magnetic Field
- 30. Induction and Inductance
- 31. Alternating Current
- 32. Electromagnetic Waves
- 33. Geometric Optics
- 34. Wave Optics
- 35. Special Relativity
13. Rotational Inertia & Energy
Energy of Rolling Motion
Back13. Rotational Inertia & Energy
Energy of Rolling Motion
- Multiple Choice
A hollow sphere of mass M and radius R rolls without slipping on a horizontal surface with angular speed W. Calculate the ratio of its linear kinetic energy to its total kinetic energy.
- Open QuestionAn airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airplane's engine is first started, it applies a constant torque of 1950 N•m to the propeller, which starts from rest. (e) What is the instantaneous power output of the motor at the instant that the propeller has turned through 5.00 revolutions?
- Open Question(a) Compute the torque developed by an industrial motor whose output is 150 kW at an angular speed of 4000 rev/min.
- Open QuestionAn electric motor consumes 9.00 kJ of electrical energy in 1.00 min. If one-third of this energy goes into heat and other forms of internal energy of the motor, with the rest going to the motor output, how much torque will this engine develop if you run it at 2500 rpm?
- Open QuestionA 2.80-kg grinding wheel is in the form of a solid cylinder of radius 0.100 m. (a) What constant torque will bring it from rest to an angular speed of 1200 rev/min in 2.5 s?