ISNS 3371 Phenomena of Nature Angular Momentum associated

ISNS 3371 - Phenomena of Nature Angular Momentum associated with rotational or orbital motion angular momentum = mass x velocity x radius

ISNS 3371 - Phenomena of Nature Torque and Conservation of Angular Momentum Conservation of angular momentum - like conservation of momentum in the absence of a net torque (twisting force), the total angular momentum of a system remains constant Torque - twisting force

ISNS 3371 - Phenomena of Nature The Moving Spool Four forces: weight (mg), upward normal force (N), tension in paper (T), and friction force ( N). If spool not yet moving, net horizontal force is zero or: Tcos( ) = N Only two of the forces produce a torque about the center of the spool (T and N). Equating the torques gives: r 1 T = r 2 N Dividing into previous equation gives cos( ) = r 1/ r 2 This gives the critical angle which determines which way the spool will rotate

ISNS 3371 - Phenomena of Nature Conservation of Angular Momentum Conservation of angular momentum - like conservation of momentum in the absence of a net torque (twisting force), the total angular momentum of a system remains constant. Newton’s Third Law of Rotation Motion: For every torque that one object exerts on a second object, there is an equal but oppositely directed torque that the second object exerts on the first object.

ISNS 3371 - Phenomena of Nature A spinning skater speeds up as she brings her arms in and slows down as she spreads her arms because of conservation of angular momentum

ISNS 3371 - Phenomena of Nature Angular Momentum associated with rotational or orbital motion: angular mom = mass x velocity x radius. The angular momentum vector is pointed along the axis of rotation - right-hand rule: curl the fingers of your right hand into a fist and point your thumb up. If the direction of your fingers is the direction of rotation, the angular momentum vector is pointed along your thumb Note: The angular momentum of a rigid body (a hoop, cylinder, etc…) is the sum of the angular momentums of the particles composing the body

ISNS 3371 - Phenomena of Nature Moment of Inertia The property of a body that is a measure of its rotational inertia - resists a change in angular (rotational) velocity (and thus angular momentum) analogous to mass - a measure of body’s translational inertia which resists a change in translational velocity/momentum - determined by mass and distribution of mass - how far the mass is from center of rotation Torque = moment of inertia X angular acceleration This is analogous to F = ma vt, at Angular acceleration measures how fast angular velocity changes r = vt/r is the angular velocity = at/r is the angular acceleration so = r

ISNS 3371 - Phenomena of Nature

ISNS 3371 - Phenomena of Nature Matter and Energy

ISNS 3371 - Phenomena of Nature Matter DEFINITION: • Anything that occupies space and has mass PROPERTIES OF MATTER: • Mass - a measure of a body’s resistance to a change in its state of motion - its inertia • Density - mass per unit volume • Dimensions - height, length, width • Electric charge - positive/negative/neutral • Heat content - everything above absolute 0 (-459. 67º F) has heat no such quantity as cold - only absence of heat • Resistance to flow of electric current - flow of charged particles electrons • Pressure - exerted by moving molecules in all directions - resists compression

ISNS 3371 - Phenomena of Nature Energy Definition of Energy: • Anything that can change the condition of matter • Ability to do work – the mover of substance (matter) • Work is a force acting over a distance • Force: The agent of change – push or pull on a body Hence: Work is the change in the energy of a system resulting from the application of a force acting over a distance. Work = force X distance Units of Energy: Joule = amount of work done when a force of 1 Newton is applied over 1 meter 1 J = 1 N - m = 1 kg m 2/s 2 1 Joule = 1/4184 Calorie, so 2500 Cal = 1 x 107 J (average daily requirement for a human)

ISNS 3371 - Phenomena of Nature Energy �Comparisons Solar energy striking Earth’s surface per second = 2. 5 x 1017 J. Energy released by burning 1 liter of oil = solar energy striking square 100 m on a side in 1 second

ISNS 3371 - Phenomena of Nature Fundamental Forces of Nature Four Types of Forces: • Gravitational – holds the world together • Electromagnetic – attraction/repulsion of charged matter • Strong Nuclear – holds nucleus together • Weak Nuclear – involved in reactions between subatomic particles

ISNS 3371 - Phenomena of Nature Energy Three basic categories: Mechanical Energy { Kinetic energy = energy of motion KE = 1/2 mv 2 Potential energy = stored energy gravitational, chemical, elastic, electrostatic, etc… Radiative - energy carried by light

ISNS 3371 - Phenomena of Nature Potential Energy One form of potential energy is gravitational potential energy - the energy which an object stores due to its ability to fall • It depends on: – the object’s mass (m) – the strength of gravity (g) – the distance which it falls (h) PE = mgh Before the sun was formed - matter contained in cloud diffuse gas cloud - most far from the center large gravitational energy. As cloud contracted under its own gravity - gravitational energy converted to thermal energy until hot enough to ignite nuclear fusion g m h

ISNS 3371 - Phenomena of Nature Potential Energy • energy is stored in matter itself • this mass-energy is what would be released if an amount of mass, m, were converted into energy E = mc 2 [ c = 3 x 108 m/s is the speed of light; m is in kg, then E is in joules] The mass energy in a 1 -kg rock is equal to as much energy as 7. 5 billion liters of oil = enough to run all the cars in the U. S. for a week A 1 -megaton hydrogen bomb converts only about 3 ounces of mass into energy.

ISNS 3371 - Phenomena of Nature Conservation of Energy • Energy can be neither created nor destroyed. • It merely changes it form or is exchanged between objects. • This principle (or law) is fundamental to science. • The total energy content of the Universe was determined in the Big Bang and remains the same today.

ISNS 3371 - Phenomena of Nature Types of Energy cannot be created or destroyed, only changed – Mechanical – • Potential - stored energy • Kinetic- energy of motion KE=1/2 mv 2 – Electrical – Chemical – Elastic – Gravitational – Thermal – Radiant – Nuclear

ISNS 3371 - Phenomena of Nature Conversion of Energy Throwing a baseball Nuclear energy (nuclear fusion on sun) - Radiative energy (sunlight) - Chemical energy (photosynthesis) - Chemical energy in pitcher’s body (from eating plants) - Mechanical kinetic energy (motion of arm) - Mechanical kinetic energy (movement of the baseball). Thus, ultimate source of KE in baseball is mass energy stored in hydrogen of Sun - created in Big Bang. Hydroelectric dam Gravitational - mechanical - electrical Nuclear reactor Nuclear - thermal - mechanical - electrical Car Chemical - thermal - mechanical

ISNS 3371 - Phenomena of Nature Power: Rate of change of energy Power = work done/time interval = E/ t (remember: means a change in a quantity) Power: 1 watt = 1 J/s Thus for every second a 100 W light bulb is on, the electric company charges for 100 J of energy. The average daily power requirement for a human is about the same as for a 100 -W light bulb.

ISNS 3371 - Phenomena of Nature Applications of Conservation of Energy

ISNS 3371 - Phenomena of Nature Machines can be used to multiply force: (force X distance)input = (force X distance)output Decrease the distance and the force will increase. Work/Energy is not changed!

ISNS 3371 - Phenomena of Nature Levers Fulcrum is in the center: d 1 = d 2 so F 1 = F 2 Fulcrum is closer to one end: d 1 > d 2 So F 2 > F 1 Give me a long enough lever and a place to put the fulcrum and I can move the world (Archimedes, 250 BC).

ISNS 3371 - Phenomena of Nature Pulleys

ISNS 3371 - Phenomena of Nature Pendulum solution (you are not expected to know this) For small angles, sin = This becomes the differential equation: vt, at r = vt/r is the angular velocity = at/r is the angular acceleration so = r With solution For a complete oscillation: so