# 1 1d kinematics x(t) = x0 + v∆t v(t) = v0 + a∆t x(t) = x0 + v0∆t + 1 2 a ...

Mechanics

Nov 13, 2013 (4 years and 5 months ago)

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1
1d kinematics
x(t) = x
0
+vΔt
v(t) = v
0
+aΔt
x(t) = x
0
+v
0
Δt +
1
2
a(Δt)
2
v
2
(x) = v
2
0
+2aΔx
2d kinematics
￿r =￿r
0
+￿v
0
t +
1
2
￿at
2
x(t) = x
0
+v
0x
t +
1
2
a
x
t
2
y(t) = y
0
+v
0y
t +
1
2
a
y
t
2
￿v =￿v
0
+￿at
v
x
(t) = v
0x
+a
x
t
v
y
(t) = v
0y
+a
y
t
Forces
￿
￿
F = m￿a
￿
F
x
= ma
x
￿
F
y
= ma
y
￿
￿
￿
￿
F
fr
￿
￿
￿ = µ
K
N
￿
￿
￿
￿
F
sfr
￿
￿
￿
≤ µ
s
N
F
g
≡ W = m× g
￿￿￿￿
=9.8m/s
2
on earth
circular motion
a
c
=
v
2
R
towards the center
θ =
s
R
ω =
Δθ
Δt
=
Δs
Δt
1
R
=
v
R
Work
W =
￿
F ∙
￿
Δx = |F| |Δx| cos(θ)
Power =
W
Δt
=
￿
F ∙ ￿v
￿
W = ΔKE KE =
￿
1
2
m
i
v
2
i
￿
W
ext
+ W
springs
+W
grav
￿
￿￿
￿
−ΔPE
springs
+ −ΔPE
grav
= ΔKE
￿
W
ext
= ΔKE +ΔPE
spring
+ΔPE
grav
PE
spring
=
1
2
kx
2
PE
grav
= mgh
Momentum& Collisons
￿p = m￿v
￿
I = ￿p
f
− ￿p
i
=
￿
￿
Fdt =
￿
F
ave
Δt
1d & 2d inelastic and elastic collisions
￿
P
total init
=
￿
P
total ﬁnal
m
1
￿v
1i
+m
2
￿v
2i
= m
1
￿v
1f
+m
2
￿v
2f
1d & 2d elastic collisions
1
2
m
1
v
2
1i
+
1
2
m
2
v
2
2i
=
1
2
m
1
v
2
1f
+
1
2
m
2
v
2
2f
1d elastic ONLY
v
1i
−v
2i
= −(v
1f
−v
2f
)