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Material Type: Notes; Class: INTRODUCTORY MECHANICS; Subject: Physics (Univ); University: Western Kentucky University; Term: Unknown 1989;
Typology: Study notes
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Vectors
2 2 A = Ax +A y
−
x
y
1
A =Axi ˆ^ +Ayˆ j
R = A+B=( Ax +Bx)iˆ+(Ay+By)jˆ=Rxiˆ+Ry jˆ
Motion in one dimension
∆x =x 2 −x 1
t
x
t t
x x v (^) av x ∆
2 1
2 1
dt
dx
t
x v t
x = ∆
∆ → 0
lim
t
v
t t
v v a
x x x av x ∆
2 1
2 1
dt
dv
t
v a
x x
t
x = ∆
∆ → 0
lim
2
2
dt
d x
dt
dx
dt
d
dt
dv a
x x =
v (^) x = v 0 x+ax⋅ t
2 0 0 2
x =x +vx ⋅t+ ⋅ax⋅t
2 0
2 v (^) x =vx+ ⋅ax⋅ x−x
t
v v x x
x x ⋅
0 0
Circular motion
r
v arad
2
= , dt
d v a
tan^ =
2
2 4
arad
Motion in two or three
dimensions
r xi yi z k
t
r
t t
r r vav ∆
2 1
2 1
dt
d r
t
r v t
∆ → 0
lim
k dt
dz j dt
dy i dt
dx
dt
d r v
t
v
t t
v v aav ∆
2 1
2 1
dt
d v
t
v a t
∆ → 0
lim
k dt
dv j dt
dv i dt
dv
dt
d v a
x (^) ˆ yˆ zˆ = = + +
2
2
dt
d x
dt
dv a
x x =^ = 2
2
dt
d y
dt
dv a
y y = =
2
2
dt
d z
dt
dv a
z z = =
k dt
d z j dt
d y i dt
d x a ˆ^ ˆ ˆ 2
2
2
2
2
2
= + +
Projectile motion
2 0 0 2
2
0
2 2 0
0 2 cos
tan x v
g y x
g
v h ⋅
sin (^0)
2 2
g
v R
0
2
Relative Velocity
vP (^) /A vP/B vB/ A