The flashcards below were created by user
rshar
on FreezingBlue Flashcards.
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Hoop or Cylindrical Shell
I = MR2
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Disk or Solid Cylinder
I = 1/2 MR2
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Disk or Solid Cylinder (axis at the rim)
I = 3/2 MR2
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Long Thin Rod (axis through midpoint)
I = 1/12 ML2
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Long Thin Rod (axis at one end)
I = 1/3 ML2
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Hollow Sphere
I = 2/3 MR2
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Solid Sphere (axis at the rim)
I = 7/5 MR2
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Solid Plate (axis through center, in plane of plate)
I = 1/12 ML2
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Solid Plate (axis perpendicular to plane of plate)
I = 1/12 M(L2 + W2)
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Rotational Kinematics (angular velocity)
ωf = ω0 + αt
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Rotational Kinematics (theta 1)
Θf = Θ0 + 1/2 (ω0 + ωf)t
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Rotational Kinematics (theta 2)
Θf = Θ0 + ω0t + 1/2αt2
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Rotational Kinematics (Angular Velocity 2)
ωf2 = ω02 + 2αΘ
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Centripetal Acceleration
acp = rω2
Centripetal acceleration is due to a change in direction of motion.
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Tangential Acceleration
at = rα
Tangential acceleration is due to a change in speed.
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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.
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Angular Position
- Θ = s/r
- s = arc length
- r = radius
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Angular Velocity
ω = ΔΘ/Δt
Θ in radians/sec
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Angular Acceleration
α = Δω/Δt
Rate of change of angular velocity
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Period of Rotation
T = 2π/ω
T = time required to complete one full rotation if the angular velocity is constant
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Rotational Kinetic Energy
Krot = 1/2 Iω2
I = moment of inertia
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Kinetic Energy of Rolling Motion
K = 1/2 mv2 + 1/2 Iω2
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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