CH8 Rotational Motion What is the Rotational velocity

CH-8: Rotational Motion What is the Rotational velocity of Earth?

Equations Sheet MOTION Rotational t (d = rθ) θ (v = rω) ω = θ/t (a = rα) α = Δω/t ω = ω0 + αt ω2 = ω02 + 2αθ θ = ω0 t + ½ αt 2 θ = ½(ω + ω0)t torque = Rotational inertia = I =mr 2 τnet = Iα L = I·ω ΣIiωi = ΣIfωf To create Inertia Linear t d; v = d/t; a = Δv/t; v = v 0 + at v 2 = v 02 + 2 ad d = v 0 t + ½ at 2 d = ½(v + v 0)t force = F Mass =m Newton’s 2 nd Law Momentum Conservation of momentum Fnet = ma p = m·V Σmivi = Σmfvf Kinetic Energy Translational Kinetic Energy = TKE = ½ mv 2 W=F·d Time interval Displacement Velocity Acceleration Kinematic equations Work Rotational Kinetic Energy = RKE = ½ Iω2 W=τ·θ

Torque, τ Torque depends on the applied force and lever-arm. Torque = Force x lever-arm Torque is a vector. It comes in clockwise and counter-clock wise directions. Unit of torque = N • m

Application of Torque: Weighing

Rotational Inertia rotational inertia = mass x square of distance from axis. I =mr 2 Rotational inertia is a scalar. Unit for I = kg. m 2

Rotational Inertia of a baton

Expressions for Several objects

Angular Momentum or Rotational Momentum Angular momentum is the product of the rotational inertia and rotational velocity. L = I·ω Conservation of Angular Momentum

Angular momentum and Bicycles