# Physics

 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) 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/rs = arc lengthr = 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 Krot = 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) Authorrshar ID50781 Card SetPhysics DescriptionRotational Kinematics Formulas Updated2010-11-20T23:06:36Z Show Answers