Ch 14: Angular MomentumSee 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 (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: Conservation of Angular Momentum

Example #1: Ice skater closes her arms

Practice: Suppose a diver spins at 8 rad/s while falling with a moment of inertia about an axis through himself of 3 kg m2 . What moment of inertia would the diver need to have to spin at 4 rad/s? 

BONUS: How could he accomplish this?

Example #2: Star collapses

Practice: Two astronauts, both 80 kg, are connected in space by a light cable. When they are 10 m apart, they spin about their center of mass with 6 rad/s. Calculate the new angular speed they’ll have if they pull on the rope to reduce their distance to 5 m. You may treat them as point masses, and assume they continue to spin around their center of mass.

Example #3: Landing and moving on a disc

Additional Problems
A horizontal platform in the shape of a uniform disk (I = 1/2 MR  2 for an axis at its center) is rotating without friction about a vertical axis at its center. The platform has mass 8.00 kg and radius 0.400 m. The platform is initially rotating at an angular velocity of 0.300 rev/s. Then a small bag of sand with mass 6.00 kg is dropped from a small height onto the platform at its rim. The bag of sand can be treated as a point mass. What is the final angular velocity of the platform after the bag of sand has been dropped onto it?
A man holding a heavy object in each hand stands on a small platform that is free to rotate about a vertical axis. Initially he is standing with his arms outstretched and he and the platform are rotating with an angular velocity of 0.600 rad/s. With his arms outstretched, the moment of inertia of the system (man + platform + weights) is 4.00 kg•m2. Then he pulls the weights in close to his chest and the angular velocity of the rotating system becomes 1.80 rad/s. What is the moment of inertia of the system after he has pulled his arms in?
A figure skater on ice spins on one foot so there is minimal friction. She pulls in her arms and her rotational speed increases. Choose the best statement below: 1.When she pulls in her arms, her rotational kinetic energy is conserved and therefore stays the same. 2. When she pulls in her arms, the work she performs on them turns into increased rotational kinetic energy. 3. When she pulls in her arms, her angular momentum decreases so as to conserve energy. 4.When she pulls in her arms, her rotational kinetic energy must decrease because of the decrease in her moment of inertia. 5. When she pulls in her arms, her moment of inertia is conserved. 6. When she pulls in her arms, her rotational potential energy increases as her arms approach the center.
A merry-go-round spins freely when Janice moves quickly to the center along a radius of the merry-go-round. It is true to say that (A) the moment of inertia of the system decreases and the angular speed increases. (B) the moment of inertia of the system decreases and the angular speed decreases. (C) the moment of inertia of the system decreases and the angular speed remains the same. (D) the moment of inertia of the system increases and the angular speed increases. (E) the moment of inertia of the system increases and the angular speed decreases.
A playground merry-go-round has a radius of 3 m and a rotational inertia of 600 kg · m2 . It is initially spinning at 0.8 rad/s when a 20 kg child starts crawling from the center toward the rim. When the child reaches the rim, what is the new angular speed of the merry-go-round? Ignore the friction force on the axle of the merry-go-round. A. 1.1 rad/s B. 0.73 rad/s C. 0.8 rad/s D. 0.62 rad/s  E. 0.89 rad/s
A thin uniform cylindrical turntable of radius 3 m and mass 25 kg rotates in a horizontal plane with an initial angular speed of 7.9 rad/s. The turntable bearing is frictionless. A clump of clay of mass 12 kg is dropped onto the turntable and sticks at a point 1.1 m from the point of rotation. Find the angular speed of the clay and turntable. A. 7.75532 B. 5.75699 C. 6.99693 D. 11.0707 E. 7.097 F. 8.15289 G. 8.35556 H. 4.96894 I. 8.6087 J. 9.56476
A sticky ball collides with and sticks to rod that is floating free in space. Consider the system of the ball and the rod, and let E be the kinetic energy of the system, p the linear momentum of the system, and L the angular momentum of the system. List which of these quantities are conserved about the point where the putty strikes the rod.1. p; E2. L3. L; E4. L; p; E5. E6. p7. L; p8. none
The sketch shows the top view of a merry-go-round which is rotating clockwise. A child jumps on the merry-go-round in three different ways:  the child lands the same distance from the center. Compare the magnitudes of the final angular momenta of the merry-go-round. I) from the left,  II) from the top, and  III) from the right. For all three cases,  1. LI = LII < LIII 2. LI > LII > LIII 3. LI = LII > LIII 4. LIII > LI > LII 5. LI = LIII < LII 6. LII > LI > LIII 7. LI = LIII > LII 8. LIII > LII > LI 9. LII > LIII > LI 10. LI > LIII > LII