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Hoop or Cylindrical Shell

I = MR²
Disk or Solid Cylinder

I = 1/2 MR²
Disk or Solid Cylinder (axis at the rim)

I = 3/2 MR²
Long Thin Rod (axis through midpoint)

I = 1/12 ML²
Long Thin Rod (axis at one end)

I = 1/3 ML²
Hollow Sphere

I = 2/3 MR²
Solid Sphere

I = 2/5 MR²
Solid Sphere (axis at the rim)

I = 7/5 MR²
Solid Plate (axis through center, in plane of plate)

I = 1/12 ML²
Solid Plate (axis perpendicular to plane of plate)

I = 1/12 M(L²+ W²)
Rotational Kinematics (angular velocity)

ω_f = ω₀ + αt
Rotational Kinematics (theta 1)

Θ_f = Θ₀ + 1/2 (ω₀ + ω_f)t
Rotational Kinematics (theta 2)

Θ_f = Θ₀ + ω₀t + 1/2αt²
Rotational Kinematics (Angular Velocity 2)

ω_f² = ω₀² + 2αΘ
Tangential Speed

v_t = rω
Centripetal Acceleration

a_cp = rω^{2

Centripetal acceleration is due to a change in direction of motion.}
Tangential Acceleration

a_t = rα

Tangential acceleration is due to a change in speed.
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.
Angular Position
- Θ = s/r
- s = arc length
- r = radius
Angular Velocity

ω = ΔΘ/Δt

Θ in radians/sec
Angular Acceleration

α = Δω/Δt

Rate of change of angular velocity
Period of Rotation

T = 2π/ω

T = time required to complete one full rotation if the angular velocity is constant
Rotational Kinetic Energy

K_rot = 1/2 Iω²

I = moment of inertia
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)

Author

rshar

50781

Card Set

Physics

Description

Rotational Kinematics Formulas

Updated

2010-11-20T23:06:36Z

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