Physics
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Hoop or Cylindrical Shell
I = MR^{2}

Disk or Solid Cylinder
I = 1/2 MR^{2}

Disk or Solid Cylinder (axis at the rim)
I = 3/2 MR^{2}

Long Thin Rod (axis through midpoint)
I = 1/12 ML^{2}

Long Thin Rod (axis at one end)
I = 1/3 ML^{2}

Hollow Sphere
I = 2/3 MR^{2}

Solid Sphere
I = 2/5 MR^{2}

Solid Sphere (axis at the rim)
I = 7/5 MR^{2}

Solid Plate (axis through center, in plane of plate)
I = 1/12 ML^{2}

Solid Plate (axis perpendicular to plane of plate)
I = 1/12 M(L^{2 }+ W^{2})

Rotational Kinematics (angular velocity)
ω_{f} = ω_{0} + αt

Rotational Kinematics (theta 1)
Θ_{f} = Θ_{0} + 1/2 (ω_{0} + ω_{f})t

Rotational Kinematics (theta 2)
Θ_{f} = Θ_{0} + ω_{0}t + 1/2αt^{2}

Rotational Kinematics (Angular Velocity 2)
ω_{f}^{2} = ω_{0}^{2} + 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 Iω^{2}
I = moment of inertia^{ }

Kinetic Energy of Rolling Motion
K = 1/2
mv^{2} + 1/2
Iω^{2}
^{can also be written as }
 K = 1/2 mv^{2} + 1/2 I (v/r)^{2 }
 = 1/2 mv^{2} ( 1 + I/mr^{2})