University:
Santa Fe College
Course:
PHY 2004 | Applied Physics 1
Academic year:

2024
Views:

172

Pages:

5
Author:

Jabin F.

#Properties of PB -> Same as CB [{A, B} = 0] [{A, {B, C}} = -{B, {A, C}}] [{[A, B], C} + {[B, C], A} + {[C, A], B} = 0] (Jacobi Identity) If α, β are some constants then: [{αA, βB} = αβ{A, B}] [{αA, B} = α{A, B}] [{A, αB} = α{A, B}] P-21 CT, defined by F(ϕ, t) = (r - r₀)² tanϕ is 2 Solution: For this, we have two different kinds of solution as: P = -∂F/∂ϕ = -(r - r₀)² sec²ϕ q = -∂F/∂t = 0 tan²ϕ = q ϕ = tan⁻¹√q For eq (1) P = -(r - r₀)² sec²ϕ = -(r - r₀)²(1 + tan²ϕ) = -(r - r₀)²(1 + q) P-126 There are two masses, each are placed at the point (a, a) and 9 masses, each are placed at the point (a, -a). The principal moment of inertia of the system is: Solution: Firstly let us check whether given co-ordinates are P.A. or not. [I_{xy} = -\sum m_{i}x_{i}y_{i} = -[ma² - ma² + ma² - ma²]] [= 0] So given co-ordinates are at P.A. axes axes and shown in figure are symmetric, so these are P.A. ∴ Principal MI are I₁ & I₂. [I₁ = Σmᵢrᵢ² = m(0)² + 9m(5a)² + m(0)² + 9m(5a)² = 8ma²] [I₂ = Σmᵢrᵢ² = m(5a)² + 9m(0)² + m(5a)² + 9m(0)² = 4ma²]