CSET - Physics Ion

Newton's 1st Law of Motion

The Law of Inertia

An object will stay at rest/remain in uniform motion (constant velocity) unless acted upon by an unbalanced force

Inertia is an object's resistance to a change in motion

Inertia

- an object's resistance to a change in motion

Newton's 2nd Law of Motion

f = ma

acceleration = (net force)/(mass)

Force is directly proportional to acceleration and mass

1 newton = 1kg*m/s^2

- This law says that external forces cause objects to accelerate

- the amount of acceleration is directly proportional to the net force acting on the objects

- the amount of acceleration is inversely proportional to the mass of the objects

- larger objects take greater forces to accelerate them

Newton's 3rd Law of Motion

- For every action there's an equal/opposite reaction

- if body A exerts a force on body B, body B exerts an equal but opposite force back onto body A

- a large mass undergoing a small acceleration and a small mass undergoing a large acceleration can be created by exactly the same amount of force

Speed

how fast an object moves, regardless of direction

rate of change of DISTANCE with respect to time

speed = d/t

DISTANCE is the amount of ground covered; it's a scalar quantity with magnitude, thus speed has a scalar quantity

Velocity

- How fast something gets somewhere WRT direction; how fast an object moves WRT direction

- Rate of change in DISPLACEMENT with respect to time

- speed, with direction

- v=dt

- DISPLACEMENT is a VECTOR quantity; thus velocity is a vector quantity (magnitude AND DIRECTION)

distance vs. displacement

- Distance is a scalar quantity and is a part of the SPEED formula

- Displacement is a VECTOR quantity and is part of the VELOCITY formula

Acceleration

- Acceleration is a vector quantity (has mag and dir)

- A is the rate at which an object changes in velocity

- units are meters per seconds squared (m/sec^2)

Average Acceleration

- the change in velocity during some measurable time interval divided by that time interval

a = (vf - vi)/(tf - ti)

acceleration = (final velocity - initial velocity)/(final time - initial time)

Ellastic Collision

- A collision where no energy is gained or lost

- objects bounce off one another

Newton's Law of Universal Gravitation

- Objects attract each other with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

- All objects that have mass exert gravitational force on every other object in the universe

- gravity depends only on MASS and DISTANCE

F = G (m1m2) /d^2,

where F is the gravitational force, G is the universal gravitational constant 6.67 x 10^-11 Nm^2/kg^2, m is the mass of each object, and d is the distance between their centers.

- it's not just how far the objects are from each other - it's the square of that distance

- EXPONENTIAL DECREASE

G

the universal gravitational constant

6.67*10^-11 NM^2/kg^2

inverse-square law

- the force between two objects will decrease exponentially as they move farther apart from each other

- this is because force is inversely proportional to the square of distance

- described by newton's universal law of gravity and the equation for getting gravitational force (you divide by (distance)^2)

F = G (m1m2) / d^2

Universal Gravitation Formala

F=Gm1m2/d^2

G = 6.67*10^-11

F = force of gravity

m = masses

d = distance between center of each object

Gravity

A force of attraction between objects that is due to their masses.

Every object exerts energy on every object

Coulomb's Law

F = k(q1q2/r^2)

- q1 and q2 are respective amounts of charge carried.

- k = electrostatic constant

- r = distance between the two objects

The objects exert equal forces on each other (so object 2 exerts the same amount of force on object 1 and object 1 does on object 2)

- The force between charged particles is dependent on TWO factors:

1) The distance between particles

2) the amount of electric charge they carry

Specifically, the force is DIRECTLY RELATED to the product of the two charges.

Force is inversely related to distance between objects (if distance increases, force will decrease).

Distance affects force more than charge.

Coulomb

- the SI unit of electric charge

- the quantity of electricity conveyed in one second by a current of one ampere.

Force

- Any influence that causes an object to change its shape or motion

balanced forces

- equal forces acting on one object in opposite directions (results in an object at rest)

- forces are at equilibrium

Friction

- a force acting in the opposite direction of motion when two objects come into contact with each other

- occurs when two objects rub against each other

Unbalanced Force

- an external force that changes the state of motion of the object

Penny Lab

- a lab that demonstrates Newton's First Law by showing that a penny will fall straight down when the vertical forces become unbalanced

- truly balanced forces can be difficult to achieve

You put a penny on top of a card that's covering a cup. You quickly remove the card and see the penny fall

free body diagram

- a diagram showing all the forces acting on an object

- special kind of vector diagram

- vectors are proportionally long to reflect strength

- draw either a box or a dot to represent the object

normal force (Fn)

- The perpendicular force exerted by a surface on an object in contact with it

- a force that acts on an object making contact with a surface in a direction perpendicular to the surface

- always equal in magnitude/opposite in direction to gravity

- balances the weight of an object on a surface

air resistance

- force that opposes the motion of objects that move through the air

- friction that acts on an object in the air

Applied force

- force applied to one object from another

Tension

- force exerted through a fully stretched object

Spring force

- force exerted by a compressed spring

Electric force

- attraction/repulsion between two charged objects

- cause electric fields (which fill up the space around every electric charge or group of charges)

Magnetic force

- exerted between two magnetic poles

periodic motion

- any motion that repeats at regular time intervals

- motion can be described with a sine or cosine curve (spends more time at the top and the bottom of its curve)

- any movement of an object that is repeated in a given length of time

- "time period" of a periodic motion is the time it takes for an object to get back to its original position

- frequency is measured in hertz; number of complete cycles per each second

"time period" of a periodic motion

- time it takes for an object to complete one full cycle of motion

- T = 2(pi)*sqrt(m/k)

T = time period of one oscillation

k - spring constant

frequency for a periodic motion

- number of complete cycles per second

- if time period of a motion is .2 seconds, the frequency is 5 hertz (there are 5 .2-second cycles in each second)

Frequency (Hz) = (angular frequency (rad/s)/2pi

Frequency = 1/T where T is the time period of oscillation in second.

Simple Harmonic Motion

- any motion where a restoring force is applied that is proportional to the displacement, in the opposite direction of that displacement (the more you pull it one way, the more it wants to return toward the middle)

- when an object moves back and forth around a middle/equilibrium position

- classic example: mass on spring, pendulum (with negligible string mass), vibrating tuning fork

- sines and cosines

- involves maximum and minimum displacement

Velocity is GREATEST IN THE MIDDLE

Acceleration (restoring force) is GREATEST AT THE EDGES

Amplitude

- MAXIMUM DISPLACEMENT on either side of the equilibrium (midpoint) position (for pendulum etc)

displacement = A(sin(omega*t))

omega = angular frequency

Angular Frequency

- The number of radians of oscillation that are completed each second, where 2π radians represents a complete cycle, measured in radians per second

- represented as an omega (fancy w) in the SHM formulas

- a full 360 degrees is 2pi radians

Angular vs. regular frequency

Regular frequency is the number of full cycles per second.

Frequency (Hz) = (angular frequency (rad/s)/2pi

Divide angular frequency by 2pi to find how many cycles occur per second.

frequency as related to time period of oscillation in seconds

F = 1/T

T = 1/F

Inverse relationship

Projectile

Any object that is given an initial velocity and then follows a path determined entirely by GRAVITATIONAL ACCELERATION

Projectile Motion

- predictable parabolic path

- influenced only by INITIAL LAUNCH SPEED, LAUNCH ANGLE, and ACCELERATION DUE TO GRAVITY

Uniform circular motion

- motion in a circle at a constant speed

- occurs because of centripetal force, force that points towards the center of a circle

Centripetal force

- a force pointing toward the center of a circle

- velocity direction is along perimeter of circle (tangential at each point)

- acceleration direction is in towards center

Formula for centripetal force:

F(c) = (mv^2)/r

centripetal force formula

Fc=mv^2/r

velocity in circular motion

v = 2πr/T

Static Equilibrium

- when an object is stationary

- sum of all forces AND sum of all torques acting on the object are equal to zero (torque is angular force)

- dynamic equilibrium is when F and T both = 0 but the object is moving at a constant rate

Translational Motion

- motion that involves sliding of an object in one or more of the three dimensions: x, y, or z

- doesn't involve things that rotate (opposite is rotational)

Rotational Motion

- motion of a body that spins around an axis in a rotational way (not necessarily sliding in one direction along any axis)

- example: ice skater bringing arms in toward body accelerating the ice skater, this is because energy is conserved and ice skater is decreasing radius, increasing speed

-

Torque

- force that causes rotation by acting off-center

- in rotational motion problems, replace F with T

- example: Newton's 1st law applied to rotations says that "a spinning body will stay spinning and non-spinning body won't start spinning UNLESS acted upon by an unbalanced TORQUE"

Rotational Motion Quantities (compare to translational)

Translational/Rotational:

- linear acceleration/angular acceleration

- force/torque

- momentum/angular momentum

- velocity/angular velocity

- mass/moment of inertia

Angular Velocity

- omega

- omega = velocity/radius

Kinetic energy formula (rotational)

KE (rotational) = (1/2)(I)(w^2) where I = MOMENT OF INERTIA and w = angular velocity

KE rotational is measured in JOULES

Moment of Inertia

- the rotational equivalent of mass

- related to shape, mass distribution, and rotational axis

Meters conversion

1 centimeter = 10 mm

1m = 100cm = 1,000mm

1km = 1000m = 100,000cm

Moment of Inertia (I) of a cylinder with uniform mass distribution

I(cylinder with uniform mass) = (1/2)mr^2

Law of Conservation of Energy

- Energy cannot be created or destroyed

- PE(gravity) = KE(translational) + KE(rotational)

Potential energy formula (gravitational)

PE=mgh

Kinetic energy formula (translational)

KE=1/2mv^2

Relative Motion

- movement in relation to a frame of reference

- must have a common reference point

Velocity of object B to A equals the velocity of object B WRT ref point + velocity of object A WRT ref point

Relative Acceleration

Comparison of the acceleration of two bodies or, for a rigid body, the point on the rigid body in reference to another point on it

Rigid Body

- a body that doesn't flex, has a constant shape

Fluids

- liquids and gases

- liquids are incompressible; gases are compressible

- all fluids have DENSITY

density

- property of fluids (liquids and gases)

- amount of matter in a given space for that substance

d=m/v

pressure

- force exerted over a given area

- depth/elevation affects pressure bc there's more weight pushing down if you go lower

P=F/A

(for static pressure)

q = 1/2pv^2

(for dynamic pressure)

buoyancy

- upward force from a fluid

viscosity

- the resistance of a fluid to flow

- depends on temperature

surface tension

- the force that acts on the surface of a liquid and that tends to minimize the area of the surface

dynamic pressure formula

q = 1/2pv^2 where p = fluid density and v = velocity of the fluid

e.g. moving through a pipe

only applicable for INCOMPRESSIBLE fluids like water or oil

static pressure formula

p = F/A

hydrostatic pressure

- Pressure at a given depth exerted by a volume of fluid against a wall, membrane, or some other structure that encloses the fluid.

- can be determined when a LIQUID IS AT REST

P = rhogd

P = pressure, rho (which looks like a p) = density of the liquid, g = gravity and d = depth

density of water

1000kg/m^3

Pascal

- SI unit of pressure

- same as kg/m^2

kinetic energy (definition and types)

- the energy an object has due to its motion

- motion exists in every object

- related to MASS and SPEED

KE = 1/2mv^2

TYPES

- vibrational: energy of motion generated by objects that vibrate, like VIOLIN STRINGS

- rotational: energy of an object rotating

- translational: energy that is passed from one object to the next (e.g. collisions)

potential energy (definition and types)

- stored energy; the object's capacity

GRAVITATIONAL PE:

PE(grav) = mgh

ELASTIC PE:

- PE that is stored in an object that is stretched like a spring

ELECTRICAL PE:

-

Mechanical energy

- energy associated with the motion or position of an object

- comes in two primary types: potential and kinetic

system

- a situation in which no external forces are at work

- could be as small as a cell or as large as the earth

momentum

LINEAR:

- mass*velocity

- represented by "p"

- is conserved

p = mv

ANGULAR MOMENTUM:

- moment of inertia*rotational velocity

kgm/s

law of conservation of momentum (definition and formula for solving problems)

- only moves from one place to another since it's neither created nor destroyed

- law stating that the total momentum of a system does not change if no net force acts on the system

In a collision,

p(initial) = p(after)

- because p = mv, we can say that

(m1v1+m2v2)initial = (m1v1+m2v2)final

pendulum

- a weight hung from a stationary point that swings freely back and forth

- simple pendulum treats the string as one that has NEGLIGIBLE MASS, thus they are an example of simple harmonic motion (SHM)

- Tension of string and gravity are the forces that act on a pendulum and keep it swinging

Where are velocity and acceleration greatest in simple harmonic motion?

Velocity is GREATEST IN THE MIDDLE

Acceleration (restoring force) is GREATEST AT THE EDGES

Time period of a pendulum (T)

T = 2pi(sqrt(L/g))

L = length of the string

g = 9.8 on earth

spring-block oscillator

- more complicated than a pendulum

- this is block hanging on a spring

what does it mean when spring constant is bigger / smaller

k = spring constant, a larger k means a stiffer spring

inverse of frequency in spring

time period

(f = 1/t, t = 1/f)

angular momentum

- "L," measured in kgm^2/s

L = (moment of inertia)*(angular velocity, omega)

L = mvrsin(theta)

m = mass (kg)

v = velocity (m/s)

r = radius of orbit/circle (m)

theta = angle between the velocity and the radius, degrees/radians

angular momentum of an object in orbit

L = mvrsin(theta)

m = mass (kg)

v = velocity (m/s)

r = radius of orbit/circle (m)

theta = angle between the velocity and the radius, degrees/radians

in a perfectly circular orbit, theta = 90 degrees so sin(90) = 1 and that part just disappears

what is the angle in a perfectly circular orbit

90 degrees, so the sin(theta) part of the equation for angular momentum of an object in orbit turns into just "1"

Inelastic collision

- a type of collision in which the kinetic energy after the collision is less than the kinetic energy before the collision because the objects stick together

- KINETIC ENERGY IS NOT CONSERVED

- MOMENTUM IS CONSERVED

KE is conserved in elastic collisions but not inelastic

parallel axis theorem

I = Icm + mh²

moment of inertia of an object around a particular axis is equal to the moment of inertia around a parallel axis that goes through the center of the mass, plus the mass of the object, multiplied by the distance to that parallel axis, squared

Rotational inertia

aka MOMENT OF INERTIA

represents how much mass a rotating object has, and how that mass is distributed

an object with more rotational inertia is harder to accelerate

measured in KGm^2

hair standing up electrical charge phenomena

- hair strands have same charge, so they repel each other

- when air is cold and dry, this is more likely to happen

- when there is a lot of moisture in the air, hair picks up charges from the air (moisture) more easily, stands up more dramatically

- when you slide down a slide, electrons are transferred to the slide

Electric Charge

- an electrical property of matter that creates electric and magnetic forces and interactions

- due to protons and electrons

ion

- a charge atom

- has different number of electrons and protons

- if there are more electrons, it's negatively charged ion. and vice versa

balloon hair example

- your hair is charged in a way that it wants to give electrons; balloons are charged in a way that it wants to accept electrons

- hair gives balloon electrons and they are attracted to each other

conservation of charge

- charges are neither created nor destroyed

- only transfers from one place to the other

static electricity

- buildup of charges on an object

- the stationary accumulation of charge on an object that can result in a spark, which is the rapid transfer of electrons between objects

electric field

- the force that fills the space around ever electric charge or group of charges

- electric fields are caused by electrical forces

- can be either static or dynamic

- electric fields are analogous to magnetic fields resulting from forces acting upon magnetic substances/poles

- size of an electric field depends only on the size of the charge that is CREATING the field - not on the size of the charge used to measure the field (the test charge)

STRENGTH OF AN ELECTRIC FIELD FORMULA:

E = F/q

E = electric field strength (newtons/coulomb)

electromagnetic waves

- have both electric and magnetic fields that are coupled to each other

- A form of energy that can travel through space

- transverse waves consisting of changing electric fields and changing magnetic fields

electrostatic fields

- electric fields that are STATIC

- produced by two stationary charges and are uncoupled to magnetic fields

dielectric material

-insulator (air, glass, plastic)

- no current flows through the material

-introduced between the plates of a capacitor

- increases capacitance by a factor called dielectric constant (k)

AC/DC

- alternating vs. direct current

- DC voltage source is connected to two conducting plates, charges of equal/opposite polarity transferred to the surfaces of the conductors

- AC voltage fluctuates sinusoidally with time