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

2024
Views:

245

Pages:

5
Author:

Jabin F.

# M.I. of Solid Cylinder: [Diagram of a solid cylinder with rings] I = MR²/2 Compiling rings on each other (hollow cylinder) Compiling disks on each other (solid cylinder) M.I. along axis of cylinder (solid): I = MR²/2 Same form as disk. M.I. along transverse axis on mid-point: When l shrinks to zero it became disk → I = MR²/2 When r shrinks to zero it became rod → I = ML²/12 I = I₁ + I₂ = MR²/4 + ML²/12 = M(R²/4 + L²/12) Q3: A hollow cube has side 'a' and mass per unit area σ. Calculate its M.I. about an axis through the center and parallel to two faces of the cube. Solution: We have to calculate M.I. at a distance of a/2 from the plane of the square for 2 faces and M.I. at a distance of a/√2 from the plane of the square for the remaining 4 faces. M = σa² I₁ = I₂ = Ma²/6 I₃ = I₄ = I₅ = I₆ = Ma²/18 I = I₁ + I₂ + I₃ + I₄ + I₅ + I₆ I = 2Ma²/6 + 4Ma²/18 I = (6Ma² + 8Ma²) / 18 I = 14Ma²/18 I = 7Ma²/9 Q: 3 rods, each mass m and length l, are joined together to form an equilateral triangle. Calculate M.I. about the axis shown. Solution: I₁ = I₂ = I₃ = ml²/12 I = I₁ + I₂ + I₃ = 3 * (ml²/12) = ml²/4