Transcript Physics 321 Hour 9 Curvilinear Systems and Central Forces

Physics 321
Hour 9
Curvilinear Systems and Central Forces
Book on a Cylinder
Book on a Cylinder
Book on a Cylinder
θ
rθ sinθ
𝑦𝑐𝑚 = 𝑟 + 𝑏 cos 𝜗
+𝑟𝜗 sin 𝜗
θ
θ
r
(r+b)cosθ
Book on a Cylinder
𝑌 = 𝑟 + 2𝑏 cos 𝜗
−(𝑎 − 𝑟𝜗) sin 𝜗
θ
θ
θ
r
θ
r cosθ
(a-r θ)sinθ
2bcosθ
Examples
• potentials4_7.nb
• potentials4_7b.nb
Bead on a Wire
If the bead slides without friction, the wire does no work. Why?
1
𝐸0 = 𝑇 + 𝑈 = 𝑚𝑣 2 + 𝑚𝑔𝑦(𝑥)
2