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

ISNS 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 Phenomena of Nature 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 The Moving Spool

ISNS Phenomena of Nature 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. Conservation of Angular Momentum

ISNS 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 Phenomena of Nature Angular Momentum 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 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 v t, a t r  = v t /r  is the angular velocity  = a t /r  is the angular acceleration so  =  r  Angular acceleration measures how fast angular velocity changes

ISNS Phenomena of Nature

Matter and Energy

ISNS Phenomena of Nature 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 ( º 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 Matter

ISNS 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 = 1N - m = 1 kg m 2 /s Joule = 1/4184 Calorie, so 2500 Cal = 1 x 10 7 J (average daily requirement for a human)

ISNS Phenomena of Nature Solar energy striking Earth’s surface per second = 2.5 x J. Energy released by burning 1 liter of oil = solar energy striking square 100 m on a side in 1 second Energy Comparisons

ISNS Phenomena 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 Fundamental Forces of Nature

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

ISNS 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 m h g

ISNS 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 10 8 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 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 Phenomena of Nature Types of Energy Energy cannot be created or destroyed, only changed –Mechanical – Potential - stored energy Kinetic- energy of motion KE=1/2mv 2 –Electrical –Chemical –Elastic –Gravitational –Thermal –Radiant –Nuclear

ISNS 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 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 = 1J/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. Power

ISNS Phenomena of Nature Applications of Conservation of Energy

ISNS Phenomena of Nature Machines 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 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 Phenomena of Nature Pulleys

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