Ch 11: Rotational Inertia & EnergyWorksheetSee all chapters
All Chapters
Ch 01: Units & Vectors
Ch 02: 1D Motion (Kinematics)
Ch 03: 2D Motion (Projectile Motion)
Ch 04: Intro to Forces (Dynamics)
Ch 05: Friction, Inclines, Systems
Ch 06: Centripetal Forces & Gravitation
Ch 07: Work & Energy
Ch 08: Conservation of Energy
Ch 09: Momentum & Impulse
Ch 09: Linear Momentum and Collisions
Ch 10: Rotational Kinematics
Ch 11: Rotational Inertia & Energy
Ch 12: Torque & Rotational Dynamics
Ch 13: Rotational Equilibrium
Ch 14: Angular Momentum
Ch 15: Periodic Motion (NEW)
Ch 15: Periodic Motion (Oscillations)
Ch 16: Waves & Sound
Ch 17: Fluid Mechanics
Ch 18: Heat and Temperature
Ch 19: Kinetic Theory of Ideal Gasses
Ch 20: The First Law of Thermodynamics
Ch 21: The Second Law of Thermodynamics
Ch 22: Electric Force & Field; Gauss' Law
Ch 23: Electric Potential
Ch 24: Capacitors & Dielectrics
Ch 25: Resistors & DC Circuits
Ch 26: Magnetic Fields and Forces
Ch 27: Sources of Magnetic Field
Ch 28: Induction and Inductance
Ch 29: Alternating Current
Ch 30: Electromagnetic Waves
Ch 31: Geometric Optics
Ch 32: Wave Optics
Ch 34: Special Relativity
Ch 35: Particle-Wave Duality
Ch 36: Atomic Structure
Ch 37: Nuclear Physics
Ch 38: Quantum Mechanics

Concept #1: Rotational Dynamics of Rolling Motion

Practice: A hollow sphere 10 kg in mass and 2 m in radius rolls without slipping along a horizontal surface with 20 m/s. It then reaches an inclined plane that makes 37° with the horizontal, as shown. If it rolls up the incline without slipping, how long will it take to reach its maximum height? (Hint: You will need to first calculate its acceleration)

Additional Problems
A thin-walled hollow sphere with mass M = 2.00 kg and radius R = 0.05 00 m has a moment of inertia of I = 2/3 MR2 for rotation about an axis through its center. Initially the sphere is rolling without slipping on a level horizontal surface and its center of mass has a translational speed of vcm = 8.00 m/s. The sphere then rolls without slipping up a ramp that is inclined at 37° above the horizontal. What is the magnitude of the friction force that the ramp exerts on the sphere while the sphere is rolling up the ramp?
A solid uniform cylinder (I = 1/2 MR2) with mass 2.00 kg and radius 0.120 m is released from rest at the top of a ramp that is inclined at 36.9° above the horizontal. The length of the ramp is 1.80 m. What is the magnitude of the static friction force required for the cylinder to roll without slipping?
A solid uniform sphere with mass 3.00 kg and radius 0.400 m is released from rest at the top of a ramp that is inclined at 36.9° above the horizontal. The sphere rolls without slipping as it moves down the ramp. As it moves down the ramp, what is the acceleration of its center of mass?
A spool is being unwound by a constant force F pulling on a string. The spool rolls without slipping. The spool has a radius r, mass m and moment of inertia I =2/3 mr2. If the spool rolls without slipping, what is the ratio of the magnitude of the applied force F to the magnitude of the friction force f, F/f? 1. 2/3 2. 1/5 3. 3/2 4. 1/7 5. 1 6. 1/3 7. 7 8. 5 9. 5/3 10. 3/5