Linear motion Circular motion S x Speed V

Linear motion Circular motion S, x θ Speed V = ΔS / Δt ω = Δθ / Δt Acceleration a = ΔV / Δt α = Δω / Δt m I = ∑m. R 2 Displacement Inertia

A) t B) t (1/2) t 2 C) 2= 2+2 A student sees the following question on an exam: A flywheel with mass 120 kg, and radius 0. 6 m, starting at rest, has an angular acceleration of 0. 1 rad/s 2. How many revolutions has the wheel undergone after 10 s? Which formula should the student use to answer the question?

Linear motion Circular motion S, Δx Δθ Speed V = ΔS / Δt ω = Δθ / Δt Acceleration a = ΔV / Δt α = Δω / Δt m I = ∑m. R 2 F, force τ , torque Work F×Δx τ×Δθ Kinetic energy ½ m. V 2 ½ Iω2 Displacement Inertia Acceleration×Inertia

Energy conservation Sphere: Spherical shell: Cylinder: Hoop: ½ m. V 2 + ½ Iω2 I = 2/5 MR 2 I = 2/3 MR 2 I = 1/2 MR 2 I = MR 2 mgh

Linear motion Circular motion S, Δx Δθ Speed V = ΔS / Δt ω = Δθ / Δt Acceleration a = ΔV / Δt α = Δω / Δt m I = ∑m. R 2 F, force τ , torque Work F×Δx τ×Δθ Kinetic energy ½ m. V 2 ½ Iω2 m. V Iω Displacement Inertia Acceleration×Inertia Momentum

A: IA= 2 IB B: 2 IA = IB C: IA = IB D: IA = 4 IB E: 4 IA=IB Consider two masses, each of size m at the ends of a light rod of length L with the axis of rotation through the center of the rod. The rod is doubled in length. What happens to I? m m 2 L L L m A 2 L m B

No external torques: L=const Momentum conservation L = Iω Consider two masses, each of size m at the ends of a light rod of length L rotating around the vertical axis with angular speed ω. During rotation the rod is doubled in length, while no external torque is applied. How does angular speed change? ω What about Energy? m L L m A ½ω m 2 L 2 L m B

HW. Chapter 8. 6, 8. 7 Quizzes and Examples!!! Problems 43, 44, 51, 52, 56