u1: kinematics Flashcards
what happens when a vector is multiplied?
the length changes but direction stays the same
what happens when a vector is multiplied by -1?
direction changes by 180: opposite direction
adding vectors: A+B
- tail to tip
- resultant: start to finish
subtracting vectors: A-B
- tail to tail, resultant: arrow points to initial
- A+(-B): draw B with opposite direction tail to tip, resultant: start to finish
what must you do when adding/subtracting vectors in drawings?
include the angle
(extend line of one arrow until it touches and measure angle)
formula for resultant displacement using pythagorean theorem
dR = SQRT(d1)^2(d2)^2
formula for finding angle using tan inverse
theta = (tan-)(d2/d1)
or opp/adj
which directions are typically negative numbers when doing component analysis?
west and south
sum of x and y components formula for position vector A
- A = AxX + AyY
- final x and y have hats to signify “units”
avg acceleration formula
aavg = (vf-vi)/t
what MUST be included in givens when solving 2D displacement Qs
deltadR = deltad1+deltad2
what must you include when calculating the magnitude of components
direction
where does theta go
between dR and initial vector
what is everything relative to
the ground
all motion is…
relative
V(AB) represents….
A relative to B
what is motion dependent on
- the point of view we describe the motion from
- also known as FOR: frame of reference
most common frame of reference
earth
what do we assume earth is?
- stationary
- it isn’t actually
what MUST you include in relative velocity Qs?
- analysis (use chain rule)
step one in relative velocity Qs
state variables
if you have V(AB), what is V(BA)?
- inverse velocity (direction)
- V(AB) = -V(BA)
if a wind is coming from the west, wht direction is it going?
east
whats a projectile
any object thts thrown/launched/dropped and moves freely through earth’s gravitational field
horizontal velocity is….
constant
vertical acceleration is….
constant
vertical motion and horizontal motion are…
independent of each other
what kind of path results from a horizontal launch
parabolic path
horizontal direction
- velocity(x) is constant
- V(i)(x) = V(f)(x)
- so, we can use:
d(x) = V(x)t
vertical direction
- acceleration (9.8m/s2 down)
- HORIZONTAL LAUNCH: V(i)(y) = 0
- use:
dy = v(iy)t + 1/2a(y)t^2 - final velocity:
v(f) = v(iy) + a(y)t
conditions for projectile motion
- motion in horizontal and vertical are independent
- object moving freely in gravitational field
- object follows a parabolic trajectory
- motion conditions:
- vertical: constant acceleration
- horizontal: constant velocity
first step in projectile problems
- diagram
- +y +x axis/scale
how do u do direction for the velocities of projectiles?
degree above/below the horizontal
cheat equations for vertical launches when d(y) = 0
t(T) = (2V(i)sintheta)/g
d(x)=(V(i)^2sin2theta)/g
when launching problem is perfect parabola, how do u find final velocity?
final velocity = initial velocity but opposite direction
- bc symmetrical parabola
when does uniform circular motion occur
when object moves in circular path at constant magnitude, not direction
is there acceleration tangentially in circular motion?
no, because speed is constant
where is acceleration i circular motion directed
radially inward and acts to change velocity direction
centre-seeking acceleration:
centripetal acceleration
a(c) = v^2/r
a(c): instantaneous acceleration
v = speed
r: radius of circular path (m)
T stands for
period (time for one revolution, seconds)
frequency
- number of cycles in one second
- Hz or s^-1
velocity vector in circular motion
- constant in magnitude
- directed tangent to the path
when solving 2D displacement, wht must u include
dR=d1+d2
when solving 2D velocity, wht must u include
v=v2-v1
v2=v+v1
v1=v2-v
whats a vector
quantities with magnitude and direction
what units do u use in scale diagrams
label as km (or wtv given in question) not cm
