Ch 11: Rotational Inertia & EnergySee 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 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 (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: Intro to Moment of Inertia

Practice: A system is made of two small masses (MLEFT = 3 kg, MRIGHT = 4 kg) attached to the ends of a 5 kg, 2-m long thin rod, as shown. Calculate the moment of inertia of the system if it spins about a perpendicular axis through the mass on the left.

Example #1: Moment of inertia of Earth

Practice: A solid disc 4 m in diameter has a moment of inertia equal to 30 kg m2 about an axis through the disc, perpendicular to its face. The disc spins at a constant 120 RPM. Calculate the mass of the disc.

Example #2: Inertia of planet of known density

Additional Problems
Two spheres, A and B, have the same mass and radius. However, sphere B is made of a dense core and a less dense shell around it. How does the moment of inertia of sphere A about its center of mass compare to the moment of inertia of sphere B about its center of mass? Ia. IA > I B Ib. IA < I B Ic. IA = I B If the two spheres are rolled down an incline from the same height simultaneously,  IIa. sphere A reaches the bottom first. IIb. sphere B reaches the bottom first. IIc. spheres A and B reach the bottom simultaneously. Choose the correct pair of statements. 1. Ic,IIa 2. Ib,IIc 3. Ib,IIb 4. Ia,IIb 5. Ia,IIa 6. Ic,IIc 7. Ib,IIa 8. Ic,IIb 9. Ia,IIc
The figure below depicts a thin rod of length 2 m and having a mass of 1000 g with three small spheres attached that have a mass of 200 g each. What is the moment of inertia for this object rotating about an axis perpendicular to the rod at its end? (The middle sphere is at the center of the rod.) A. 20 kg m2 B. 30/23 kg m2  C. 3√2 kg m2 D. 11/15 kg m2 E. 7/3 kg m2
A diatomic molecule such as molecular nitrogen (N2) consists of two atoms each of mass M, whose nuclei are a distance d apart. What is the moment of inertia of the molecule about its center of mass?A. M d 2B. 2M d 2C. 4M d 2D. 1/2 M d 2 E. 1/4 M d 2
A rotating object is formed by wrapping a cylinder with a thin plastic. The cylinder has a mass of 12 kg, a radius of 15 cm, and a height of 25 cm. The plastic wrap has a mass of 4 kg and is assumed to have a zero thickness. If the object rotates about the central axis of the cylinder, what is the moment of inertia of the object?
A baton is made of a 10 cm rod with a mass of 500 g, with two 70 g masses attached to each end. What is the moment of inertia of the rod when it rotates about an axis, perpendicular to its length, halfway down the rod?
A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m. What is the moment of inertia of this system of masses about the x-axis? a. 160 kg•m2 b. 90 kg•m2 c. 250 kg•m2 d. 32 kg•m2