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In this introductory lecture, Professor Lewin discuses basic units, dimensions, measurements and associated uncertainties, dimensional analysis, and scaling arguments. Further, he explains why a measurement is meaningless without knowledge of its uncertainty, using data collected by Galileo Galilei as an example. He begins to dive into dimensional analysis, reasoning that the time from an object to fall from a certain height is independent of its mass and proportional to the square root of the height from which it is dropped. He confirms this conclusion by dropping an apple from various heights.
This lecture is an introduction to kinematics which ultimately leads (in Lecture 4) to trajectories in three-dimensions. Professor Lewin begins with a description of one-dimensional motion of a particle. He talks about average velocity, the importance of + and - signs, and our free choice of origin. He moves into a conversation about average speed vs. average velocity, instantaneous velocity (reviewing when velocity is zero, positive, and negative), and instantaneous acceleration. He shoots a bullet through two wires, calculating the average speed from the distance between the wires and the elapsed time.
This lecture is about vectors and how to add, subtract, decompose and multiply vectors. Decomposing vectors in two (or three) dimensions is a key concept that will be used throughout the course. Professor Lewin throws an object up, and decomposes its initial velocity into a horizontal and a vertical direction.
This lecture is all about motion of projectiles (if air drag can be ignored). The objects experience a constant vertical acceleration due to the acceleration of gravity (see also Lecture 12). Professor Lewin reviews the equations for projectile motion, showing that the trajectory is a parabola. He continues with a demonstration that shows how to measure the initial speed of a projectile and how to reach maximum horizontal distance shooting a ball.
This lecture is about uniform circular motion. There is a constant radial acceleration (centripetal acceleration) but constant tangential speed. Professor Lewin uses himself as an example, sitting on a chair bolted to a fast rotating turntable feeling the push and pull of centripetal force. He continues with discussion of the motion of the planets around the sun, with respect to gravitational pull, and the idea behind a centrifuge and a salad spinner. He concludes with a demonstration that emphasizes centripetal acceleration, spinning a buck of water fast enough that the water will put even when upside down. To be on the safe side, bring an umbrella to class!
This lecture is all about Newton's First (inertia), Second (F=ma) and Third (action=-reaction) Laws. He builds on past discussion of vector forces, moving on to decompose forces in the x and y directions. As the class comes to an end, Professor Lewin ends with a bizarre demo involving two identical strings, one suspending a mass, the other suspending from the mass. Which one breaks when you pull on the lower string, the upper string or the lower string? Professor Lewin pulls a fast one!
This lecture explores weight, perceived gravity, weightlessness, free fall, and zero perceived gravity in orbit. An object is swirled around on a string in a vertical plane. The tension in the string is evaluated when the object is at the top and when it is at the bottom of its circular trajectory. Objects in free fall as described as weightless: Exploring the weight of a tennis ball being tossed in the air, and of a bottle of water in Professor Lewin's hands when he jumps off a table. The bottle and Lewin are in free fall, thus both are weightless.
This lecture deals exclusively with frictional forces. Starting with a block at rest on a horizontal surface, Professor Lewin describes the normal force, the maximum frictional force that must be overcome to budge the block, and the coefficient of static friction. He continues to make measurements of the coefficient of static friction, and presents ways to reduce friction using hydroplanes and air tracks. Even a flea can move a very heavy book if the friction is zero (as demonstrated).
This lecture reviews selected topics previously covered in lectures 1 through 5. This includes: scaling arguments, dot products, cross products, one-dimensional kinematics, trajectories, and uniform circular motion. Professor Lewin concludes by presenting a brain teaser to the audience. Sliding his fingers underneath a yardstick, towards the center, something strange happens: the fingers seem to make turns moving, they alternating sliding and stopping. Can you explain this?
Concepts covered in this lecture begin with the restoring force of a spring (Hooke's Law) which leads to an equation of motion that is characteristic of a simple harmonic oscillator (SHO). Using the small angle approximation, a similar expression is reached for a pendulum. To demonstrate that the period is independent of the mass of the bob, Professor Lewin places himself at the end of the 5 meter long cable and measures the period.
The concepts introduced are: work, conservative forces, potential energy, kinetic energy, mechanical energy, and Newton's law of universal gravitation. A wrecking ball is converting gravitational potential energy into kinetic energy and back and forth. If released with zero speed, the wrecking ball should NOT swing higher than its height when it was released. Professor Lewin puts his life on the line by demonstrating this.
This lecture covers resistive forces such as air drag. It includes the viscous (linear in velocity) and pressure (quadratic in velocity) terms. Quantitative demonstrations with balloons and with ball bearings dropped in syrup are shown. He concludes with numerical calculations of air drag examples, also discussing the contribution of air drag to the quantitative experiments down earlier in the course with falling apples.
In this lecture, Professor Lewin displays how the conservation of mechanical energy can be used to derive the equation of motion for simple harmonic oscillators (SHO). In doing so he covers gravitational potential energy, equilibrium points where the net force is zero, parabolic potential energy, and circular potential energy.
In this lecture, bound and unbound orbits are discussed. Professor Lewin begins with a description of escape velocity, or the minimum speed required to escape the gravitational pull. Various sources of energy, energy storage, energy conversion, and the world's energy consumption are discussed. Power, or the rate at which a force does work on an object, is central to the conversation. Professor Lewin concludes with a few words on global energy consumption and sources: although the US has about 1/30 of the world's population, it accounts for 1/5 the global energy consumption. He considers harvesting solar radiation and nuclear power to fix this energy crisis.
Momentum and its conservation during collisions is introduced. Kinetic energy can decrease or increase during collisions. When kinetic energy is conserved, we call it an elastic collision. The momentum vector, internal forces, external forces and the conservation of momentum are discussed. Professor Lewin does some air track experiments where the released energy is from a compressed spring; kinetic energy increases but momentum is conserved. The definition of the center of mass is described. The center of mass behaves as if all the matter were together at that point.
In this lecture Professor Lewin covers elastic and inelastic collisions, including a discussion on center of mass and internal inergy. He concludes with a Newton's Cradle demonstration, soliciting an analytical proof of his demo showing a lineup of colliding balls.
The momentum of individual objects can change in a variety of ways. Professor Lewin covers a number of topics in this lecture, including impulse and thrust. An analogy is drawn between the force felt by the target of a tomato thrower, the reaction force felt by the thrower, and the propulsion (thrust) of a rocket.
This lecture reviews selected concepts previously covered in lectures 6 through 15. Professor Lewin covers work-energy theorem, pendulum energy, simple harmonic oscillators, Newton's Law of Universal Gravitation, resistive forces, and finally collisions and conservation of momentum. At the beginning of class a top is spun on the desk in the lecture hall to show that friction dissipates the top's kinetic energy into heat, and the top quickly falls over. Professor Lewin then spins the same top on a small magic black box and the top does not fall over! At the end of the class the top is still spinning: what's going on?
Rotating Rigid Bodies, Moments of Inertia, Parallel Axis and Perpendicular Axis Theorem. The moment of inertia for a rigid body around an axis of rotation is introduced, and related to its rotational kinetic energy. Flywheels can be used to store energy. Planets and stars have spin rotational kinetic energy, and the Crab Nebula pulsar is presented as a spectacular example.
Angular momentum (a vector) is introduced. The rate of change of angular momentum is related to the torque (also a vector). In the absence of an external torque, angular momentum is conserved. Spin angular momentum (of planets, stars, neutron stars) is also discussed.
In the absence of a net external torque on an object, angular momentum is conserved. When an object oscillates about an axis of rotation, there is a variable restoring torque acting on the object. A review is given of equations for angular momentum and torque, and the importance of choosing the point of origin. These equations are exercised using an example of a circular orbit.
Kepler's Laws, Elliptical Orbits, Change of Orbits, and the famous passing of a Ham Sandwich by astronauts in orbit. Kepler's three Laws summarize the motion of the planets in our solar system. Following Newton's law of universal gravitation, the conservation of angular momentum and mechanical energy allow us to calculate the semimajor axis of the elliptical orbits, the orbital period and other orbital parameters. All we have to know is one position and the associated velocity of a planet and the entire orbit follows.
Doppler Effect, Binary Stars, Neutron Stars and Black Holes. Doppler shift is introduced with sound waves, then extended to electromagnetic waves (radiation). The Doppler shift of stellar spectral lines and/or pulsar frequencies provides a measure of the line-of-sight (so-called radial) velocity of the source relative to the observer. Combined with Newton's law of universal gravitation, this can lead to the orbital parameters and the mass of both stars in a binary star system.
In this lecture, Professor Lewin covers the rate of change in angular momentum through the use of rolling motion and gyroscopes. When you apply a torque to a fast spinning wheel, it moves the spin angular momentum in the direction of the torque (torque is a vector). This is called precession. A suitcase is brought in that requires special handling. There is a fast rotating flywheel inside! A student volunteers to carry the suitcase around. The suitcase behaves in a weird manner as the student turns around.
Static equilibrium is covered in this lecture, achieved only when the net external force AND net external torque on an object are both zero. A ladder leaning against the wall is analyzed to determine the minimum angle it can make with the floor without sliding. Professor Lewin continues with the topic by discussing how to locate the center of mass of a rigid body. The center of mass always lines up below the point of suspenson such that the net torque is zero. He concludes by discussing the stability of a ropewalker, improved by lowering her center of mass below the rope.
In this lecture Processor Lewin introduces elasticity and Young's modulus. The fractional length deformation of a material (the strain) depends on the force per unit area (the stress). The stress vs. strain dependence is described conceptually, then explored empirically. The speed of sound in a material depends on the stiffness and density of the material; from this follows the fundamental frequency at which a rod resonates. Professor Lewin cocludes with a demo in which a 2kg block is suspended from one string, and an identical string is suspended from the block. Professor Lewin pulls on the lower string. Which string will break first, the upper one or the lower one? The lower string will break first if the force is impulsive (a quick jerk) because it will elongate faster than the upper string. If we pull slowly the upper string will break first as its tension will then always exceed that of the lower string.
Concepts covered in this lecture include gases and incompressible liquids, Pascal's Principle, hydrostatic and barometric pressure. Professor Lewins concludes with a discussion of overpressure in our lungs. The lung capacity, our ability to overcome hydrostatic pressure, is measured with a manometer. This is related to how deep snorkeling works, and why scuba-divers use pressurized air tanks. Professor Lewin demonstrates that by blowing on a manometer, or by sucking on it, we can raise or lower a column of water by about 1 meter (0.1 atmosphere). So why then was he able to suck fluid up a straw of several meters long?
Concepts covered in this lecture include hydrostatics, Archimedes' Principle, fluid dynamics, and Bernoulli's Equation. The buoyant foce of air on a ballon is discussed, and then Professor Lewin demonstrates how a balloon and a pendulum behave in accelerated, closed containers. The lecture ends with some non-intuitive demos shoiing how ping pong balls behave in air streams.
This lecture reviews selected concepts previously covered in lectures 16 through 24: one-dimensional collisions, simple harmonic oscillation (SHO) of a suspended rod, conservation laws for a satellite s orbit, the Doppler shift, and pure role.
The simple harmonic oscillations (SHO) of suspended solid bodies are related to their geometry. The torsional pendulum oscillates in the horizontal plane; the SHO does NOT depend on the small angle approximation. In this lecture Professor Lewin discusses the SHO equation of motion for a rigid body pendulum, for a liquid sloshing in a U-shaped tube, and for a torsional pendulum.
Systems consisting of pendulums and springs can freely oscillate at their natural frequencies (also called normal modes). When we expose a system to a wide spectrum of frequencies, the response will be very large at the normal mode frequencies (resonances) of that system. Examples include musical instruments (standing waves on violin strings and pressure waves in wind instruments), and torsional standing waves on a bridge driven by strong winds.
Heat, conductivity, and thermal expansion are the discussed in this lecture. Both linear thermal expansion, leading to a need for expansion joints in railroad rails on hot days, and cubical thermal expansion, as occurs in a mercury thermometer, are covered in detail. The lectures ends with a focus on the cubical thermal expansion of water: the density of ice is about 8% lower than water, so ice cubes and icebergs float.
The ideal-gas law is introduced, and the rate of momentum transfer from the gas molecules to the vessel walls is related to pressure. The concepts of phase diagrams and phase transitions are also introduced, and they are explored with fire extinguishers, boiling water, and cooled balloons filled with air. The ideal-gas law holds (approximately) when you have only gas; it doesn't hold whenever there is any liquid present. Professor Lewin uses a demo of water boiling at room temperature but low pressure.
This lecture is devoted to discussion of the wonderful Quantum world. Classical Mechanics, in spite of all of its impressive predictive power, fails to explain many microscopic behaviors. This led to the development of Quantum Mechanics, where electrons orbit nuclei in discrete energy levels, light can behave as a particle, and particles behave as waves. The location of microscopic particles can only be expressed in terms of probabilities. Heisenberg's uncertainty principle is discussed and demonstrated.
In this closing lecture, Professor Lewin talks about some of the highlights from his early days at MIT. It began with balloon flights at very high altitude to make observations of the stars in X-rays. This led to discoveries of X-ray flaring events and a periodic X-ray source (GX 1+4). In the seventies and eighties he made important contributions to our understanding of X-ray bursts (thermo-nuclear fusion episodes on neutron stars).
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