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Introduction
Classical Mechanics
an introductory course
Richard Fitzpatrick
Associate Professor of Physics
The University of Texas at Austin
Introduction
Major sources:
What is classical mechanics?
mks units
Standard prefixes
Other units
Precision and significant figures
Dimensional analysis
Worked example 1.1: Conversion of units
Worked example 1.2: Tire pressure
Worked example 1.3: Dimensional analysis
Motion in 1 dimension
Introduction
Displacement
Velocity
Acceleration
Motion with constant velocity
Motion with constant acceleration
Free-fall under gravity
Worked example 2.1: Velocity-time graph
Worked example 2.2: Speed trap
Worked example 2.3: The Brooklyn bridge
Motion in 3 dimensions
Introduction
Cartesian coordinates
Vector displacement
Vector addition
Vector magnitude
Scalar multiplication
Diagonals of a parallelogram
Vector velocity and vector acceleration
Motion with constant velocity
Motion with constant acceleration
Projectile motion
Relative velocity
Worked example 3.1: Broken play
Worked example 3.2: Gallileo's experiment
Worked example 3.3: Cannon shot
Worked example 3.4: Hail Mary pass
Worked example 3.5: Flight UA589
Newton's laws of motion
Introduction
Newton's first law of motion
Newton's second law of motion
Hooke's law
Newton's third law of motion
Mass and weight
Strings, pulleys, and inclines
Friction
Frames of reference
Worked example 4.1: In equilibrium
Worked example 4.2: Block accelerating up a slope
Worked example 4.3: Raising a platform
Worked example 4.4: Suspended block
Conservation of energy
Introduction
Energy conservation during free-fall
Work
Conservative and non-conservative force-fields
Potential energy
Hooke's law
Motion in a general 1-dimensional potential
Power
Worked example 5.1: Bucket lifted from a well
Worked example 5.2: Dragging a treasure chest
Worked example 5.3: Stretching a spring
Worked example 5.4: Roller coaster ride
Worked example 5.5: Sliding down a plane
Worked example 5.6: Driving up an incline
Conservation of momentum
Introduction
Two-component systems
Multi-component systems
Rocket science
Impulses
Collisions in 1-dimension
Collisions in 2-dimensions
Worked example 6.1: Cannon in a railway carriage
Worked example 6.2: Hitting a softball
Worked example 6.3: Skater and medicine ball
Worked example 6.4: Bullet and block
Worked example 6.5: Elastic collision
Worked example 6.6: 2-dimensional collision
Circular motion
Introduction
Uniform circular motion
Centripetal acceleration
The conical pendulum
Non-uniform circular motion
The vertical pendulum
Motion on curved surfaces
Worked example 7.1: A banked curve
Worked example 7.2: Circular race track
Worked example 7.3: Amusement park ride
Worked example 7.4: Aerobatic maneuver
Worked example 7.5: Ballistic pendulum
Rotational motion
Introduction
Rigid body rotation
Is rotation a vector?
The vector product
Centre of mass
Moment of inertia
Torque
Power and work
Translational motion versus rotational motion
The physics of baseball
Combined translational and rotational motion
Worked example 8.1: Balancing tires
Worked example 8.2: Accelerating a wheel
Worked example 8.3: Moment of inertia of a rod
Worked example 8.4: Weight and pulley
Worked example 8.5: Hinged rod
Worked example 8.6: Horsepower of engine
Worked example 8.7: Rotating cylinder
Angular momentum
Introduction
Angular momentum of a point particle
Angular momentum of an extended object
Angular momentum of a multi-component system
Worked example 9.1: Angular momentum of a missile
Worked example 9.2: Angular momentum of a sphere
Worked example 9.3: Spinning skater
Statics
Introduction
The principles of statics
Equilibrium of a laminar object in a gravitational field
Rods and cables
Ladders and walls
Jointed rods
Worked example 10.1: Equilibrium of two rods
Worked example 10.2: Rod supported by a cable
Worked example 10.3: Leaning ladder
Worked example 10.4: Truck crossing a bridge
Worked example 10.5: Rod supported by a strut
Oscillatory motion
Introduction
Simple harmonic motion
The torsion pendulum
The simple pendulum
The compound pendulum
Uniform circular motion
Worked example 11.1: Piston in steam engine
Worked example 11.2: Block and spring
Worked example 11.3: Block and two springs
Worked example 11.4: Energy in simple harmonic motion
Worked example 11.5: Gravity on a new planet
Worked example 11.6: Oscillating disk
Orbital motion
Introduction
Historical background
Gravity
Gravitational potential energy
Satellite orbits
Planetary orbits
Worked example 12.1: Gravity on Callisto
Worked example 12.2: Acceleration of a rocket
Worked example 12.3: Circular Earth orbit
Worked example 12.4: Halley's comet
Worked example 12.5: Mass of star
Worked example 12.6: Launch energy
About this document ...
Richard Fitzpatrick 2006-02-02
