# Angular Momentum & Conservation

## Angular Momentum

Course Material Related to This Topic:

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.

Course Material Related to This Topic:

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.

Course Material Related to This Topic:

Collision of rotating and stationary washers.

Rotational energy of a spinning figure skater.

## Conservation of Angular Momentum

Course Material Related to This Topic:

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.

Course Material Related to This Topic:

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.

Course Material Related to This Topic:

Motion of a meteor approaching and just grazing the earth.

## 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.

Course Material Related to This Topic:

## Rotational Inertia

Course Material Related to This Topic:

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.

## 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.

Course Material Related to This Topic:

## Rigid Body Dynamics Examples

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

Course Material Related to This Topic:

## 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.

Course Material Related to This Topic:

## 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.

Course Material Related to This Topic:

## Torque

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

Course Material Related to This Topic:

## Moment of Inertia

Course Material Related to This Topic:

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

Course Material Related to This Topic:

Calculating the moment of inertia of a washer.

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

## Angular Momentum of Orbits

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

Course Material Related to This Topic:

## Gyroscope

Course Material Related to This Topic:

Analogy of a precessing gyroscope to uniform circular motion.

Torque, angular velocity, and precession of gyroscopes.

## 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.

Course Material Related to This Topic:

## 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.

Course Material Related to This Topic:

## 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.

Course Material Related to This Topic:

## Experiment 9

Angular momentum experiment setup and procedure.

Course Material Related to This Topic:

## 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.

Course Material Related to This Topic:

## Tidal Locking

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

Course Material Related to This Topic:

## Rotational Dynamics

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

Course Material Related to This Topic:

## Moment of Inertia of a Uniform Disc

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

Course Material Related to This Topic:

## Turntable

Frictional torque acting on a spinning uniform circular disc.

Course Material Related to This Topic:

## Experiment 8 Analysis

Analysis of data collected in Experiment 8.

Course Material Related to This Topic:

## Platform Diving

Motion of a somersaulting diver.

Course Material Related to This Topic:

## Bohr Hydrogen Atom

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

Course Material Related to This Topic:

## Experiment 9 Analysis

Analysis of data collected in Experiment 9.

Course Material Related to This Topic:

## Rotational Collision

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

Course Material Related to This Topic:

## Hitting a Baseball

Collision of a bat with a baseball.

Course Material Related to This Topic:

## Colliding Rotating Washers

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

Course Material Related to This Topic:

## Sliding and Rolling Bowling Ball

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

Course Material Related to This Topic:

## Stick on Frictionless Plane

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

Course Material Related to This Topic:

## Merry-Go-Round

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

Course Material Related to This Topic:

## Angular Momentum and Rotational Energy

Effect of a spinning figure skater pulling in her arms.

Course Material Related to This Topic:

## Angular Dynamics

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

Course Material Related to This Topic:

## Torque and Angular Acceleration

Two masses connected by a rope wrapped around a pulley.

Course Material Related to This Topic:

## Tetherball

Kinematics and dynamics of a rotating tetherball.

Course Material Related to This Topic: