Angular Momentum & Conservation

 

Angular Momentum

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

  • Watch video clip from Lecture 20 (0:00 - 8:18)

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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.

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

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

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

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Collision of rotating and stationary washers.

Rotational energy of a spinning figure skater.

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Conservation of Angular Momentum

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

  • Watch video clip from Lecture 20 (8:18 - 17:36)

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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.

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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.

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Motion of a meteor approaching and just grazing the earth.

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Ice Skaters' Delight

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

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Stellar Equilibrium and Remnants

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

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  • Watch video clip from Lecture 20 (25:34 - 35:32)

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Revolution of the Earth

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

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  • Watch video clip from Lecture 21 (0:00 - 7:36)

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Angular Momentum of a Spinning Rod

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

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  • Watch video clip from Lecture 21 (7:36 - 14:10)

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Motion of a Rod After Impulse

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

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  • Watch video clip from Lecture 21 (14:10 - 25:40)

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Mysterious Spinner

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

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Rigid Body Kinematics

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.

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Rotational Inertia

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

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Rigid Body Dynamics

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.

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Rigid Body Dynamics Examples

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

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Work and Energy in Rotational Motion

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.

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Rolling of Rigid Bodies

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

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Torque

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

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Moment of Inertia

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

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Calculating the moment of inertia of a washer.

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

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Angular Momentum of Orbits

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

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Gyroscope

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Analogy of a precessing gyroscope to uniform circular motion.

Torque, angular velocity, and precession of gyroscopes.

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Angular Momentum of a Point Particle

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.

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Angular Momentum of a Rigid Body

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.

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Total Angular Momentum

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.

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Experiment 9

Angular momentum experiment setup and procedure.

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Rotational Dynamics Review

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.

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Tidal Locking

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

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Rotational Dynamics

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

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Moment of Inertia of a Uniform Disc

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

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Turntable

Frictional torque acting on a spinning uniform circular disc.

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Experiment 8 Analysis

Analysis of data collected in Experiment 8.

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Platform Diving

Motion of a somersaulting diver.

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Bohr Hydrogen Atom

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

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Experiment 9 Analysis

Analysis of data collected in Experiment 9.

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Rotational Collision

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

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Hitting a Baseball

Collision of a bat with a baseball.

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Colliding Rotating Washers

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

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Sliding and Rolling Bowling Ball

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

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Stick on Frictionless Plane

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

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Merry-Go-Round

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

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Angular Momentum and Rotational Energy

Effect of a spinning figure skater pulling in her arms.

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Angular Dynamics

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

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Torque and Angular Acceleration

Two masses connected by a rope wrapped around a pulley.

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Tetherball

Kinematics and dynamics of a rotating tetherball.

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