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)
ωf = ω0 + αt
Rotational Kinematics (theta 1)
Θf = Θ0 + 1/2 (ω0 + ωf)t
Rotational Kinematics (theta 2)
Θf = Θ0 + ω0t + 1/2αt2
Rotational Kinematics (Angular Velocity 2)
ωf2 = ω02 + 2αΘ
Tangential Speed
vt = rω
Centripetal Acceleration
acp = rω2
Centripetal acceleration is due to a change in direction of motion.
Tangential Acceleration
at = 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