TD3 Dynamique du solide

200 m5m/s
γT=dυ
dt = 0
γN=υ2
R=25 200 = 0.125ms−2
10 m/s
500 m
γN=υ2
R=100 500 = 0.2ms−2
80 kg
−−−−→
forces =m−→ γ−→ F=m−→ γ F =mυ2
R=
80 ×0.2 = 16 N
m= 2 kg R 0.35 m
J J =mR2= 2.(0.35)2= 0.245 kgm2
R= 0.1m m = 5 kg
J
J=1
2mR2= 0.5×5×(0.1)2= 2,5.10−2kgm2
ω= 120rads−1t= 8s α
M∆=Jα α α α =dω
dt ω=αt +cte
t= 0s ω = 0 cte = 0
α=ω
t=120 8rads−2M∆=Jα = 2,5.10−2×120 8= 0.375 Joules
m= 10g r = 0.05m
ω60000 tours/min
F=m×acc´el´eration F =mυ2
r=mr2ω2 r=mrω2
F= 10−2×5 10−2×60000
60 ×2π2
≃2 104N
m=F
g= 2 tonnes

16 m
11g g ≃10 ms−2
γN= 11g= 110ms−2=υ2
R=⇒υ=√16 ×110 = 42ms−1
ω=υ
R= 2.6rads−1≃25tours/min 2π
g= 10m/s2
J=1
2mr2
R M
r < R
O
−→
P−→ T
J M R
⇒J=1
2×2M×R2=MR2
−→
T
−→
P
−→
M(−→ T) = −→ r∧−→ T Moment =T r
−→
P
T r J
α
−−−−−→
moment =J−→ α T r =Jα −→ α
α γ

υ=rω γ =rα
−−−−→
forces =masse ×acc´el´eration −→ T+−→ P= 2M−→ γ
−T+P= 2Mγ
−T+P= 2Mγ T r =Jα J =MR2⇒T=Jα
r=MR2α r=MR2 r×γ r
⇒ −MR2
r2γ+P= 2Mγ
γ=g1 + R2
2r2−1
P= 2Mg
−MR2
r2γ+ 2Mg = 2Mγ γ =g1 + R2 2r2−1
T=2MgR2
R2+ 2r2
T=MR2
r2γ=MR2 r2×γ=MR2 r2×g1 + R2 2r2−1
T=g2r2
2r2+R2×MR2 r2r2