Chapitre 15
CHAPITRE 15
15.3 I = ML 2 /12
15.4 ω =
3g/l
15.5 a = mg/(m + M/2)
15.6 I = 22Ma 2
15.7 (a) I = mL 2 /3
(b) I = mL 2 /12
(c) I = mr 2
(d) I = mr 2 /2
15.8 F = Mg/4
15.9 W = 6mL 2 ω 2
0
15.10 (a) V 0 = r
2Mgh/(I + Mr 2 )
15.11 La boucle doit être accélérée de 2g sin θ.
15.13 I =
8
15
πρ(R
5
− r
5 ) =
2
5
M
R 5 − r 5
R 3 − r 3
15.14 μ 0 = (2/7) tan θ
15.15 (b) a = g/(1 + R 2 /2r 2 )
15.16 h = 3d/2 − 3r
15.17 (a) v 2 = (r 1 /r 2 )v 1
(b) W =
1
2 mv 2
1 (r 2
1 /r 2
2 − 1)
(c) F = mv 2 /r
15.18 (a) a = FR(R cos α − r)/(I + MR 2 )
15.19 h/r = 7/5
15.20 r 2
3 + r 2
1 = r 2
2
15.21 α max = (2g/R) cos θ
15.22 t = 2lω 0 /3μg
15.23 (a) D = 12V 2
0 /49μg
(b) V = (5/7)V 0
15.24 (a) V 0 = (2/5)Rω 0
(b) V 0 = (1/4)Rω 0
15.25 l = R(
√
1 + M/4m − 1)
15.26 (a) F
x = F x cos θ + F y sin θ + 2mω ˙
y + mω
2 x
F
y = F y cos θ − F x sin θ − 2mω ˙
x + mω
2
y
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