Physics

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Author:
rshar
ID:
50781
Filename:
Physics
Updated:
2010-11-20 18:06:36
Tags:
Rotational Kinematics Physics
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Description:
Rotational Kinematics Formulas
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  1. Hoop or Cylindrical Shell
    I = MR2
  2. Disk or Solid Cylinder
    I = 1/2 MR2
  3. Disk or Solid Cylinder (axis at the rim)
    I = 3/2 MR2
  4. Long Thin Rod (axis through midpoint)
    I = 1/12 ML2
  5. Long Thin Rod (axis at one end)
    I = 1/3 ML2
  6. Hollow Sphere
    I = 2/3 MR2
  7. Solid Sphere
    I = 2/5 MR2
  8. Solid Sphere (axis at the rim)
    I = 7/5 MR2
  9. Solid Plate (axis through center, in plane of plate)
    I = 1/12 ML2
  10. Solid Plate (axis perpendicular to plane of plate)
    I = 1/12 M(L2 + W2)
  11. Rotational Kinematics (angular velocity)
    ωf = ω0 + αt
  12. Rotational Kinematics (theta 1)
    Θf = Θ0 + 1/2 (ω0 + ωf)t
  13. Rotational Kinematics (theta 2)
    Θf = Θ0 + ω0t + 1/2αt2
  14. Rotational Kinematics (Angular Velocity 2)
    ωf2 = ω02 + 2αΘ
  15. Tangential Speed
    vt = rω
  16. Centripetal Acceleration
    acp = rω2

    Centripetal acceleration is due to a change in direction of motion.
  17. Tangential Acceleration
    at = rα

    Tangential acceleration is due to a change in speed.
  18. Rolling Motion
    ω = v/r

    Rolling motion is a combination of translational and rotational motions. An object of radius r, rolling without slipping, translates with linear speed v and rotates with angular speed.
  19. Angular Position
    • Θ = s/r
    • s = arc length
    • r = radius
  20. Angular Velocity
    ω = ΔΘ/Δt

    Θ in radians/sec
  21. Angular Acceleration
    α = Δω/Δt

    Rate of change of angular velocity
  22. Period of Rotation
    T = 2π/ω

    T = time required to complete one full rotation if the angular velocity is constant
  23. Rotational Kinetic Energy
    Krot = 1/2 2

    I = moment of inertia
  24. Kinetic Energy of Rolling Motion
    K = 1/2 mv2 + 1/2 2

    can also be written as

    • K = 1/2 mv2 + 1/2 I (v/r)2
    • = 1/2 mv2 ( 1 + I/mr2)

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