Chapter 1: Units and Kinematics Flashcards
Fundamental units of SI system; length, mass, force, time, work/energy, and power
Length: meter (m) Mass: kilogram (kg) Force: Newton (N) TIme: second (s) Work/Energy: joule (J) Power: watt (W)
Multiples and submultipes
Multiples -- giga (G) 10^9 -- mega (M) 10^6 -- kilo (k) 10^3 Submultiples -- centi (c) 10^-2 -- milli (m) 10^-3 -- micro (µ) 10^-6 -- nano (n) 10^-9 -- pico (p) 10^-12
Scientific notation: multiplication
multiply significands and add exponents
Scientific notation: division
divide significand in numerator by significand in denominator, then subtract exponent from denominator from exponent from numerator
Scientific notation: raising to a power
significand raised to the poser and exponent multiplied by that power
Scientific notation: addition and subtraction
must have same exponents; add/subtract significands and then use same exponent
Trigonometric relations: sin function of important angles
angle = sin(angle) 0 = 0 30 = 0.5 45 = sqrt2/2 =~0.707 60 = sqrt3/2 =~0.866 90 = 1 180 = 0
Trigonometric relations: cos function of important angles
angle = cos(angle) 0 = 1 30 = sqrt3/2 =~0.866 45 = sqrt2/2 =~0.707 60 = 0.5 90 = 0 180 = -1
Logarithms (definition)
the logarithm of a number to a given base is simply the power to which that base must be raised to equal that number
log(base10)x=y => 10^y = x
Rules of logarithms
log(mn) = log m + log n log(m/n) = log m - log n log(m^n) = n log m
Vectors vs scalars
Vectors = magnitude and direction Scalars = magnitude, no direction
Vector addition
(1) head to tail method: place the head of one vector next to the tail of the other vector and the resultant vector is from the tail of the first to the head of the second
(2) resolve the vectors into their components, add each component separately, use pythagorean theorem to determine the magnitude of the resultant vector and use trigonometric functions to determine the direction of the resultant function
Vector subtraction
A - B = A + (-B)
Multiplying a vector by a scalar
multiplying a vector by a scalar changes either the length, the direction, or both the length and the direction
Kinematics (definition)
branch of Newtonian mechanics that deals with the description of motion
Displacement
Change in an object’s position in space, vector quantity; does not account for the actual pathway
Velocity
rate of change of displacement in a given unit of time; vector w/ units meter/second
Speed
rate of change of distance in a given unit of time; scalar with units meter/second
Instantaneous speed and instantaneous velocity
Instantaneous speed: always the magnitude of an object’s instantaneous velocity
Instantaneous velocity: measure of the average velocity as the change in time approaches 0
Average speed and average velocity
Average speed accounts for actual distance traveled whereas average velocity does not
v(avg) = ∆x/∆t
Acceleration
rate of change of velocity over time; vector quantity w/ units m/s^2
Average acceleration
change in instantaneous velocity over the change in time; a(avg) = ∆v/∆t
Instantaneous acceleration
average acceleration as ∆t approaches zero
Motion with constant acceleration: Linear motion and equations
- motion with constant acceleration
- object’s velocity and acceleration are along the line of motion; pathway of moving object is a straight line
- equations
(1) v = v0 + at
(2) x - x0 = v0t +(1/2)at^2
(3) v^2 = v0^2 + 2a(x-x0)
(4) v(avg) = (1/2)(v0+v)
(5) ∆x = v(avg)t = (1/2)(v0+v)t - -note regarding the equations: v0 and x0 are v and x at t=0; when the motion is vertical, use y instead of x; in using the equations, remember that velocity and acceleration are vector quantities
Free fall
type of linear motion where the object’s weight is the only force acting upon it; falls with constant acceleration
Motion with constant acceleration: Projectile motion
- motion that follows a path along two dimensions
- analyze v & a separately for each component
- only y-component will experience force of gravity, so v(y) changes at the rate of g, but v(x) is constant (there is no horizontal acceleration)
