Definition; calculating L from different frames; conservation of L from circle center.

Proof that dL/dt = r × f; angular momentum conserved when τ = 0; spin angular momentum defined.

Angular momentum conservation calculation and demo for spinning person, with arms outstretched and pulled in.

Definition; white dwarf, neutron star, black hole properties; energy released in a supernova.

Conservation of angular momentum in general systems and in Earth's orbit; τ = 0 at center of revolution.

Angular momentum of a rod revolving around the center of mass and a point off the CM; conservation of L only for CM.

Speed of center of mass and angular velocity of rod after impulse at non-CM point, using two different origins; demonstration of motion.

Demonstration of blue plastic spinner that stops and spins in the opposite direction, apparently violating laws of physics.

Rotation about a fixed axis; definitions of angular velocity and angular acceleration; right-hand rule; rotational motion with constant angular accleration; relationship between angular velocity, linear velocity, and acceleration, with example.

Definition of rotational kinetic energy, with example; definition of moment of inertia for a rigid body; moment of inertia example.

Parallel-axis theorem, with example; perpendicular-axis theorem, with examples; definition of angular momentum of a particle; definition of central forces; angular momentum of a particle moving in a straight line; angular momentum of a particle in uniform circular motion; angular momentum of a conical pendulum.

Relationship between forces and angular momentum; definition of the law of conservation of angular momentum; definition of torque; angular momentum and central forces, with examples.

Torque and force; angular momentum and torque; torque and angular momentum of a conical pendulum; torque and angular acceleration; rigid body angular acceleration, with examples; torque due to gravity, with examples; conservation of angular momentum.

Rotational dynamics examples, including particle on a string and spinning bicycle wheel.

Work-energy theorem in rotational motion, with examples; angular impulse, with example; decomposition of displacement into translation and rotation; rolling motion of cylinders and spheres.

Rolling motion of a rigid body, such as a cylinder or a sphere, with several examples; angular momentum and collisions, with example; gyroscope precession.

Rotation about a fixed axis; definitions of angular velocity and angular acceleration; right-hand rule; rotational motion with constant angular acceleration; relationship between angular velocity, linear velocity, and acceleration, with example.

Definition of rotational kinetic energy, with example; definition of moment of inertia for a rigid body; table of rotational inertia values for various objects; moment of inertia example.

Parallel-axis theorem, with example; perpendicular-axis theorem, with examples; definition of angular momentum of a particle; definition of central forces; angular momentum of a particle moving in a straight line; angular momentum of a particle in uniform circular motion; angular momentum of a conical pendulum.

Relationship between forces and angular momentum; definition of the law of conservation of angular momentum; definition of torque; angular momentum and central forces, with examples.

Torque and force; angular momentum and torque; torque and angular momentum of a conical pendulum; torque and angular acceleration; rigid body angular acceleration, with examples; torque due to gravity, with examples; conservation of angular momentum.

Rotational dynamics examples, including particle on a string and spinning bicycle wheel.

Work-energy theorem in rotational motion, with examples; angular impulse, with example; decomposition of displacement into translation and rotation; rolling motion of cylinders and spheres.

Rolling motion of a rigid body, such as a cylinder or a sphere, with several examples; angular momentum and collisions, with example; gyroscope precession.

Torque defined; conditions for rotational static equilibrium; torque and rotational dynamics; moment of inertia; parallel axis theorem.

Checklist for solving torque problems; angular momentum defined, with equation; angular impulse defined, with equation.

Definition, with equation; moments of inertia for common shapes; angular momentum and moment of inertia.

Equations for angular momentum of orbiting bodies; connection of angular momentum and rotational energy to equation of orbit.

Analogy of a precessing gyroscope to uniform circular motion.

Overview of translational and rotational dynamics of a rotating point mass; angular velocity and angular acceleration vectors for fixed axis rotation; angular momentum of a point particle using cross products; right hand rule; angular momentum for fixed axis rotation; torque and the time derivative of angular momentum for a point particle.

Angular momentum and torque for a system of particles; angular momentum of a rigid body for fixed axis rotation; conservation of angular momentum about a point; total angular momentum about a fixed point.

Conditions under which momentum, energy, and angular momentum are conserved; total angular momentum about a fixed point; earth's orbital angular momentum about sun; earth's spin angular momentum; total angular momentum for Earth's motion about Sun.

Angular momentum experiment setup and procedure.

Torque, rotational kinetic energy, moment of inertia, and rotational work defined; strategy for computing moment of inertia; translational and rotational kinematics/dynamics combined; Kepler's Law for conservation of angular momentum.

Effect of tides on L and kinetic energy of earth-moon system; stable scenario for tidal system.

Solution (PDF)^#

Angular acceleration as a function of moment of inertia; motion of a rolling wheel.

Linear and angular momentum of a rotating tennis ball; parallel axis theorem; collision between a rod and a small mass; impulse and angular momentum.

Effects of changing the moment of inertia of a spinning object on angular velocity, angular momentum, and kinetic energy.

Collisions between washers spinning on the same axis.

Torque, angular velocity, and precession of gyroscopes.

Calculating the moment of inertia of a uniform circular disc about two parallel axes.

Solution (PDF)

Frictional torque acting on a spinning uniform circular disc.

Solution (PDF)

Calculating the moment of inertia of a washer.

Solution (PDF)^#

Analysis of data collected in Experiment 8.

Solution (PDF)^#

Motion of a meteor approaching and just grazing the earth.

Solution (PDF)^#

Motion of a somersaulting diver.

Solution (PDF)^#

Analysis of a hydrogen atom modeled as an electron orbiting a proton.

Solution (PDF)

Analysis of data collected in Experiment 9.

Solution (PDF)

3-part problem; bullet hits side of cylinder; finding L, ω, and v of cylinder.

Solution (PDF)^#

Effect of a child jumping onto a merry-go-round.

Solution (PDF)

Collision of a bat with a baseball.

Solution (PDF)

5-part problem; initial L and kinetic energy of washer, frictional torque, final ω of washers, average τ in collision.

Solution (PDF)^#

Calculating ω and kinetic energy for bowling ball when it begins to roll; loss of KE.

Solution (PDF)^#

4-part problem; putty inelastically collides with stick; finding CM, p, ω, distance traveled in one revolution.

Solution (PDF)^#

6-part problem; calculating α, ω, power exerted on merry-go-round; ω and kinetic energy after I changes.

Solution (PDF)^#

Effect of a spinning figure skater pulling in her arms.

Solution (PDF)^#

Collision of rotating and stationary washers.

Solution (PDF)^#

Motion of a rotating merry-go-round, before and after children move to the center.

Solution (PDF - 2.0 MB)^#

Two masses connected by a rope wrapped around a pulley.

Solution (PDF - 2.0 MB)^#

Kinematics and dynamics of a rotating tetherball.

Solution (PDF - 1.1 MB)^#

Rotational energy of a spinning figure skater.

Solution (PDF - 1.1 MB)^#

Angular acceleration of a steel washer mounted on a cylindrical rotor.

Solution (PDF - 1.1 MB)^#