Notes, summaries, assignments, exams, and problems for Physics

Torque and the Moment Arm

Torque is the turning effect produced by a force, also known as a moment. It is directly proportional to the magnitude of the force as well as the distance between the line of action of the force and the axis of rotation. In the motion of a restrained system, torque occurs when force is applied away from the axis and the line of action does not pass through the axis. Common examples include muscles, doors, wrenches, and hammers.

The moment arm is the shortest distance between the axis of rotation and the line of action. It is always perpendicular to the force's line of action and the axis of rotation.

Classification of Lever Systems

A lever consists of three primary components:

• Axis of rotation (fulcrum)
• Motive forces (muscles)

Extrasolar Planets

An extrasolar planet is a planet orbiting a star other than our Sun. There are two general ways of learning about a distant object: directly, which means by obtaining images or spectra of the object, and indirectly, which means by inferring the object’s existence or properties without actually seeing it. There are two major indirect approaches to finding and studying extrasolar planets:

1. Observing the motion of a star to detect the subtle gravitational tugs
2. Observing changes to a star’s brightness that occur when one of its planets passes in front of the star as viewed from Earth.

Planets exert gravitational tugs on their star, causing the star to orbit around the system center of mass. Gravitational tugs: we can detect a... Continue reading "Discovering Extrasolar Planets: Methods and Significance" »

What is Cosmology?

Cosmology Defined

Cosmology is the study of the origin, present structure, evolution, and density of the universe.

The Cosmological Principle

The cosmological principle is the basic assumption that physical laws are true everywhere in the universe, not just on Earth.

The Expanding Universe

Galactic Recession

We observe galaxy clusters receding from us, which implies that the universe is expanding. Galaxies farthest from us are moving away the fastest; the farther the distance, the faster the speed.

Hubble's Law

Hubble's Law states that a galaxy’s velocity of recession (v) is directly proportional to its distance from us (d). The formula is v = Hd.

The Hubble Constant

The Hubble constant (H) is a crucial value that gives the rate at... Continue reading "Cosmology Fundamentals: The Big Bang, Hubble's Law, and the Universe's Fate" »

The Proton-Proton Chain: Powering Low-Mass Stars

The proton-proton chain is the series of nuclear reactions by which low-mass stars, including our Sun, fuse hydrogen into helium. This process is crucial for stellar energy generation.

Gravitational equilibrium and energy balance work together as a natural thermostat, maintaining the Sun’s core temperature and fusion rate at a steady level.

Unraveling the Sun's Energy Source

Early scientific theories proposed that the Sun's energy came from chemical reactions or gravitational collapse. However, these theories were disproven:

• Chemical burning: Ruled out because it cannot account for the Sun’s immense luminosity.
• Gravitational collapse: The conversion of gravitational potential energy into heat as

Introduction

Transverse and Longitudinal Waves

Mechanical waves can exist only in material media and are governed by Newton's laws. Transverse mechanical waves, like those on a stretched string, are waves in which the particles of the medium oscillate perpendicular to the wave's direction of travel. Waves in which the particles of the medium oscillate parallel to the wave's direction of travel are longitudinal.

Sinusoidal Waves

A sinusoidal wave moving in the positive direction of an x-axis has the mathematical form: y(x,t) = y_m sin(kx - ωt), where:

• y_m is the amplitude of the wave.
• k is the angular wave number.
• ω is the angular frequency.
• kx - ωt is the phase.

The wavelength (λ) is related to k by k = 2π/λ.

Wave Parameters

The period T and frequency f of the... Continue reading "Understanding Mechanical and Sound Waves: Physics Principles" »

White Dwarf Stellar Explosions

Novae: Recurrent Stellar Flares

The hydrogen build-up on the surface of a white dwarf can ignite into an explosive fusion reaction that blows off a shell of gas. Because so little mass is blown off during a nova, the explosion does not disrupt the binary system. Ignition of the infalling hydrogen can recur again with periods ranging from months to thousands of years.

White Dwarf Supernovae (Type Ia)

Subrahmanyan Chandrasekhar predicted that gravity will overcome the pressure of electron degeneracy if a white dwarf has a mass > 1.4 M_¤. Energetic electrons, which cause this pressure, reach the speed of light. If accretion brings the mass of a white dwarf above the Chandrasekhar limit, electron degeneracy can no... Continue reading "Stellar Endpoints: Supernovae, Neutron Stars, and Black Holes" »

Shock Waves: Formation and Mach Cone Angle

If the speed of a source relative to the medium exceeds the speed of sound in the medium, the Doppler equation no longer applies. In such a case, shock waves result. The half-angle of the Mach cone is given by:

Temperature Measurement and Thermometers

Temperature is an SI base quantity related to our sense of hot and cold. It is measured with a thermometer, which contains a working substance with a measurable property, such as length or pressure, that changes in a regular way as the substance becomes hotter or colder.

Zeroth Law of Thermodynamics: Thermal Equilibrium

When a thermometer and some other object are placed in contact with each other, they eventually reach thermal equilibrium. The reading of... Continue reading "Fundamental Concepts in Thermodynamics and Gas Behavior" »

Irreversible Processes and Entropy (S)

An irreversible process is one that cannot be reversed by means of small changes in the environment. The direction in which an irreversible process proceeds is set by the change in entropy ($S$) of the system undergoing the process. Entropy $S$ is a state property of the system.

Fundamentals of Electric Charge

The strength of a particle's electrical interaction with objects around it depends on its electric charge, which can be either positive or negative. Charges with the same sign repel each other, and charges with opposite signs attract each other.

An object with equal amounts of the two kinds of charge is electrically neutral, whereas one with an imbalance is electrically charged.

Conductors and Insulators

• Conductors

Write your text here!Bernoulli's theorem, in fluid dynamics, relation among the pressure, velocity, and elevation in a moving fluid (liquid or gas), the compressibility and viscosity (internal friction) of which are negligible and the flow of which is steady, or laminar.