Centripetal Acceleration and Uniform Circular Motion, Study notes of Physics

Download Centripetal Acceleration and Uniform Circular Motion and more Study notes Physics in PDF only on Docsity! Uniform Circular Motion Motion in a circular path with constant radius, r, and constant speed, v. Velocity does change in direction. Then there is an acceleration. tΔ Δ = va Centripetal Acceleration if if ttt − − = Δ Δ = vvva rv rv Δ = Δ tr v Δ Δ = r a As Δr , Δt → 0 v t → Δ Δr r vac 2 = From the similarity of the velocity and radial vector triangles v rT π2= Centripetal acceleration, directed towards the center Example – 6.2 Conical Pendulum v = ? r vmmaTF cr 2 sin === θ θcosTmg = θsinLr = θ θ θ tan cos sin gr m mgrv == θθ tansingLv = Example – 6.4 What is the maximum speed of the car without skidding? m = 1500 kg rcurve = 35 m μs = 0.5 r vmmanf css 2 max max, === μ nmg = smgr m mgrv ss /1.13max === μ μ Radial and Tangential Acceleration The object changes speed and direction. Acceleration has a radial and tangential component. tr aaa += r var 2 −= dt d at v = Terminal Velocity Occurs when the resistive force equals gravity. Then the net force and acceleration is zero. The object moves at constant speed (vT). Sky divers, soap bubbles. Example 6.13 Find the resistive force on a 90 mph fastball. mbaseball = 0.145 kg 2 2 1 TAvDmg ρ= • Assume the baseball is dropped vertically and using the values in the book for vT , A and ρ, calculate the drag coefficient. • Then use this value to find R with v = 90mph. Av mgD T 2 2 ρ = 2 2 1 AvDR ρ= Review Radial acceleration: aC = mv/r2 Radial force: F = maC Viscous drag will limit velocity