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UT / Physics / PHYS 221 / What are metric multipliers?

What are metric multipliers?

What are metric multipliers?


Physics 221 Exam 1 Study Guide

What are metric multipliers?

I. Chapter 1: Introduction to Physics

A. Common Metric Multipliers

1. Kilo - 10^3

2. Deci - 10^-1

3. Centi – 10^-2

4. Mili – 10^-3

5. Micro – 10^-6

B. Trig Identities

1. sinθ = opposite/hypotenuse

2. cosθ = adjacent/hypotenuse

3. tanθ = opposite/adjacent  


4. Pythagorean Theorem: c 2 = a 2 + b 2  


What is the initial velocity of a falling object?

5. First quadrant: ALL (+), second quadrant: SIN (+), third  quadrant: TAN (+), fourth quadrant: COS (+)  


II. Chapters 2 and 3

A. By convention, (+)Y is taken to be north, and (+)X is east B. General Equations for 1D and 2D motion:If you want to learn more check out What is the difference between personal troubles and public issues?
Don't forget about the age old question of What did freud believe about phobias?

1. Δx = voxt + 1⁄2 axt2 

 vx =vox +axt

 vx2 = vox2 + 2axΔx (careful with sign of root)  

2. Δy = voyt + 1⁄2 ayt2 

How do you find the horizontal displacement of a projectile?

 vy =voy +ayt

 vy2 = voy2 + 2ayΔy (careful with sign of root)  

C. Projectile Motion: CONSTANT horizontal velocity for x &  FREE FALL in y

1. Δx = voxt Don't forget about the age old question of How does the mesosystem affect child development?

 vx =vox

2. Δy = voyt – 1⁄2 gt2 Don't forget about the age old question of What cells are autorhythmic?

 vy =voy –gt

 vy2 = voy2– 2gΔy (careful with sign of root)  

D. Reminders

1. If an object is dropped, the initial velocity is ZERO 2. If an object is projected from the ground and lands on the  ground, vertical displacement (delta y) is ZERO; total horizontal  displacement (delta x) is the RANGE Don't forget about the age old question of What are some human activities that degrade natural capital?

3. In 2D motion, when finding velocity, solve for both x AND y  components and find TOTAL velocity by using Pythagorean  theorem  

4. Properties of Free Fall:

a) object is moving ONLY under the influence of gravity (9.8m/s^2) = g = a

b) the direction of ‘a’ points straight down

c) the value for ‘g’ is positive and a can be positive or  negative  

5. Properties of Projectile Motion: given x and y and ignoring  air resistance  

a) Horizontal Acceleration is ZERO (constant velocity in  x direction)

b) Vertical Acceleration is NEGATIVE g (where  

g=9.8m/s^2 and (+)y)

6. Remember to break down a problem into x and y  components and use angles that are relative to the +x axis  (signs will be taken care of) 0-360 degrees

E. Adding/ Subtracting Vectors:

1. Ax = A cosθ

2. Ay = A sinθ

3. A = Pythagorean theorem

4. θ = arctan (Ay/Ax) If you want to learn more check out What is forced choice method of performance appraisal?

III. Chapter 4 & 5:  

A. Newton’s Laws of Motion

1. First Law of Motion: An object moves with a velocity  constant in magnitude and direction UNLESS acted upon by a  NON-ZERO net force  

2. Second Law of Motion*: The acceleration of an object is  directly proportional to the net force (sigma F) acting on it and  inversely proportional to its mass (m) a = SigmaF/m or SigmaF  = ma  

a) Break this equation down into x and y components!

3. Third Law of Motion: if object one and object two interact  with each other, the force exerted by object one on object two is  equal in magnitude and opposite in direction to the force exerted by object two on object one

B. Difference between weight and mass

1. Weight is a force that changes if g changes (W = mg);  points straight down

2. Mass is constant no matter what

C. Properties of Forces

1. Normal force (N)

a) force is exerted perpendicular to the surface

b) Electromagnetic in nature

c) Results from contact with a surface

d) No set magnitude or direction  

2. Tension Forces (T): force exerted by ropes/cables/ chains/  strings etc.

a) Does not change throughout medium

b) Points along the rope/ cable/ chain/ string…

c) No set magnitude or direction

*Normal Forces, Tension Forces, and Frictional Forces are all CONTACT FORCES*

3. Frictional Forces: result of microscopic roughness of  surfaces in contact

a) Independent of area of contact and speed of surfaces b) Direction of friction opposed the direction of motion

c) Kinetic: only with moving objects, has a definite  


d) Static: only with stationary objects, range values (0  is less than or equal to Fs is less than or equal to MusN)

*When an object is about to move, use static frictional force*

D. Stress = pressure = Force / Area

1. Shear = sliding/ grating  S*delta / h (N/m^2)

2. Bending = compression/ tension  Y*delta L/ L initial  (N/m^2)

3. Torsion = twisting  

4. Bulk = volume effect; acting in all directions  -B*delta V/ V (N/m^2)

E. Stress and Strain: Deformations

1. Elastic region: solid will return to its original shape (obeys  Hooke’s Law)

2. Plastic region: solid will NOT return to its original shape,  but atoms still connect

3. Fracture: atoms separate (ultimate strength of material is  exceeded)

IV. Chapter 6

A. Centripetal Acceleration: points toward the center of a circular  path and relates to the change in direction; centripetal force is keeping it in a circular path

1. rw^2 = v^2 / r  w is roe not weight!

2. As the radius decreases, centripetal acceleration increases, thus centripetal force increases. If velocity increases, centripetal  acceleration also increases by a factor squared

3. As long as an object has circular motion, if the linear speed changes, centripetal acceleration is still present

B. Differences between tangential acceleration and centripetal  acceleration

1. Tangential = TANGENT to circular path; related to change  in SPEED

2. Centripetal = points toward the center of the circle; related to change in DIRECTION

3. TOTAL ACCELERATION = combination of tangential  

acceleration and centripetal acceleration (Pythagorean theorem) C. Fictitious Force = centrifugal force  

1. Refers to the lack of centripetal acceleration; points away  from the center of the circle (why we lean left when turning right) D. Newton’s Law of Gravitation: attractive force of gravity between  two particles is proportional to the product of their masses and  inversely proportional to square of distance between them 1. Fg= Gm1*m2 / r^2 where G is a constant

2. Shell theorem: force of gravity OUTSIDE a sphere can be  determined by treating sphere’s mass as if it were concentrated  at the center; as mass increases, force of gravity increases, and  as distance increases, force of gravity decreases

3. Variations of g: higher elevations g gets smaller; g at  equator is slightly less than at the poles

*Density of the Earth is NOT constant*

E. Kepler’s Laws of Planetary Motion

1. First Law (“Law of Orbits”): all planets move in elliptical  orbits around the sun

a) Acceleration = (r (min) + r (max)) / 2 and  

eccentricity is a measure of elongated eclipse  e = d / a

b) Aphelion = farthest from the sun

c) Perihelion = closest to the sun

2. Second Law (“Law of Areas”): an orbiting body sweeps out  equal areas in equal amounts of time

3. Third Law (“Law of Periods”): the square of the period of an orbit is proportional to the cube of the semimajor axis of the orbit and mass of the central body

a) T^2 = (4pi^2 / GM) * a^3

b) Then square of the period (T) is related to the  

semimajor axis (a) CUBED, so if you double T, a will also  

increase, but it is not doubled!

V. Chapter 7

A. Properties of Work

1. Constant force exerted through distance does mechanical  work

2. W = (F cosθ) delta x = F * delta x (unit: J)

3. Work is positive when direction of the force is the same as  the motion, and work is negative when the force is in the  

direction that opposes motion  

*If force is perpendicular to the displacement/ direction of motion, it does NO WORK!

B. Properties of Kinetic Energy

1. K = ½mv^2 (unit: J)

2. Energy of motion

3. Network done on an object is equal to the change of kinetic energy

a) Wnet = delta k = 1/2mv (final)^2 – 1/2mv (initial)^2 C. Types of Work

1. Conservative: work done by a conservative force (path  DOES NOT matter)  gravity and springs

2. Non-conservative: work done by a non-conservative force  (path DOES matter)  friction and drag

3. W (conservative) + W (non-conservative) = delta KE D. Work done by gravity: expressed in terms of gravitational  potential energy

1. Wg = -delta PE = - (PE (final) – PE (initial))

2. Gravitational potential energy only depends on relative  height

3. PEG = mgy  

E. Properties of Spring Potential Energy

1. Hooke’s Law describes how the force on a spring is related  to the strength of the spring and the amount compressed/  stretched

2. Force of spring = -kx CONSERVATIVE FORCE (path does  not matter) and PE (spring) = ½kx^2

F. Conservation of Energy Principles

1. If some forces involved are non-conservative reduce the  KE or PE of an object due to dissipation, but the TOTAL energy of  the system remains conserved  

2. W (non-conservative) = E (final) – E (initial)

*Non-conservative forces dissipate energy THERMAL ENERGY*

G. Principles of Power

1. Average power is work divided by time it takes to do work  or force * speed (unit W = 1J/s)

2. P (av) = W / delta t OR P (av) = delta E / delta t OR P (av) = Fv (av)

H. Energy Conversion in Humans

1. The human body converts energy stored in food into work,  thermal energy, and/or chemical energy stored in fatty tissue 2. The rate at which the body uses food energy to sustain life  and do different activities is the metabolic rate 

3. Correspond rate when at rest is called the basal metabolic  rate 

I. World Energy Use

1. Fuel, natural gas, solar energy

2. Energy that can be used to do work always partly  

converted to less useful forms  

VI. Chapter 8

A. Elastic vs. Inelastic Collisions

1. Inelastic: total momentum IS constant, but the kinetic  energy IS NOT (baseball bat hitting a baseball, rubber ball hitting a wall)

a) Initial momentum = final momentum  

b) When objects collide and stick together and move  

with the same velocity  COMPLETELY inelastic collision  

(two piece of putty colliding)

2. (m1v1 + m2v2) / m1 + m2

3. Elastic: total momentum AND total kinetic energy are  constant (two pool balls colliding)

a) Initial momentum = final momentum

b) Initial kinetic energy = final kinetic energy

*When two objects with the same mass collide head-on, they switch velocities after collision*

B. Momentum: a VECTOR that points in the same direction as  the velocity and is equal to the mass of an object times its  velocity

1. p = mv

2. When there are several objects involved, the total linear  momentum is the sum of all individual momenta  p (total) = p1  + p2 + p3 + …

C. Impulse: the force acting on that object multiplied by the  time interval in which the force was acting on the object  1. I = F (av) * delta t

2. Impulse is a vector that points in the same direction as the  force

3. F (av) delta t = delta p = mv (final) – mv (initial) D. Conservation of Linear Momentum: if the net external force  acting on an object is ZERO, then the linear momentum is  CONSTANT  

1. p (final) = p (initial)

2. If a system consists of two colliding objects, then the total  momentum BEFORE the collision is EQUAL to the total  momentum AFTER the collision

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