d S(t) ---- dt |
= |
d (vt) ------ dt |
= | v |
d f(x)) ---- dx |
= |
d ax ---- dx |
= | a |
Δ S(t) ---- Δ t |
Δ S(t) ---- Δ t |
= |
6 - 2 |
= | 3 |
d S(t) ---- dt |
= |
d (vt) ------ dt |
= | v (equation 2) |
S'(t) | = |
d S(t) ---- dt |
= | speed |
S'(t) | = |
d S(t) ---- dt |
= at |
┌ 1 ┐ │ 3 │ └ 2 ┘ |
· |
┌ 0 ┐ │ 1 │ └ 0 ┘ |
= 3 |
Δr(t) ---- Δt |
= | Δv(t) (equation 7) |
dr(t) ---- dt |
= | v(t) (equation 8) |
Δv(t) ---- Δt |
= | Δ a(t) (equation 9) |
dv(t) ---- dt |
= |
d^{2}r(t) ---- dt^{2} |
= | a(t) (equation 10) |
r(t) | = | |r(t)| r_{U}(t) | = | r(t) r_{U}(t) |
v(t) | = |
d r(t) ---- dt |
= |
d r(t) ---- r_{U}(t) dt |
+ |
d r_{U}(t) ------ r(t) dt |
(equation 8' - note the accent) |
d r_{U}(t) ------ dt |
r(t) = |
┌ 2cos(t) ┐ └ sin(t) ┘ |
v(t) | = |
dr(t) ---- dt |
= |
┌ -2sin(t) ┐ └ cos(t) ┘ |
dr(t) ---- dt |
= |
dx(t) ---- e_{x} dt |
+ |
dy(t) ---- e_{y} dt |
+ |
dz(t) ---- e_{z} dt |
S'(t) | = |
d S(t) ----- dt |
= |
d (vt) ------ dt |
= | v |
S'(t) | = |
d S(t) ----- dt |
= |
d -- dt |
½ at^{2} | = | at | = | v |
dr(t) ---- dt |
= | v(t) |
dv(t) ---- dt |
= |
d^{2}r(t) ---- dt^{2} |
= | a(t) |
F_{1} = |
┌ -6 ┐ └ 0 ┘ |
F_{2} = |
┌ 12 ┐ └ 0 ┘ |
F_{R} = |
┌ -6 ┐ └ 0 ┘ |
+ |
┌ 12 ┐ └ 0 ┘ |
= |
┌ -6 + 12 ┐ └ 0 + 0 ┘ |
= |
┌ 6 ┐ └ 0 ┘ |
F_{1} = |
┌ -2 ┐ └ 5 ┘ |
F_{2} = |
┌ 1 ┐ └ -3 ┘ |
F_{R} = |
┌ -2 ┐ └ 5 ┘ |
+ |
┌ 1 ┐ └ -3 ┘ |
= |
┌ -2 + 1 ┐ └ 5 + -3 ┘ |
= |
┌ -1 ┐ └ 2 ┘ |
sin(α) = |
|F_{p}| ---- |F_{g}| |
a | = |
(v_{ AFTER} - v_{ BEFORE}) ------------- Δ t |
m a | = | m |
(v_{ AFTER} - v_{ BEFORE}) ------------- Δ t |
F | = | m |
(v_{ AFTER} - v_{ BEFORE}) ------------- Δ t |
F Δ t | = | m (v_{ AFTER} - v_{ BEFORE}) | = | mv_{ AFTER} - mv_{ BEFORE} (equation 11) |
cos(α) = |
|F_{P}| ---- |F| |
v_{T} | = |
S -- t |
= |
2πR -- T |
(equation 22) |
ω | = |
2π -- T |
= |
Δ θ -- Δ t |
(equation 23) |
v_{T} | = |
2πR -- T |
= | ωR | (equation 24) |
a_{T} | = |
v_{T}^{2} -- R |
(equation 28) |
F_{T} | = |
mv_{T}^{2} -- R |
(equation 29) |