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