Angular acceleration vs. Centripetal acceleration Angular acceleration arises when a spinning object is speeding up or slowing down its spin. (Example: A car tire as a car is speeding up) Centripetal acceleration has to do with the fact that the tangential velocity of an object is always changing even if the speed of the spin is not. (Example: Earth’s orbit around the sun) The centripetal force (which is the net force causing circular motion) always points towards the center of the circle. Circular Motion An object moving in circular motion is inherently accelerating (centripetal acceleration). "F = mac It must therefore have a net force continually acting on it. We call this net force the Centripetal Force. ! Q A car rounds a curve while maintaining a constant speed. Is there a net force on the car as it rounds the curve? (Q7-2) A car rounds a curve while maintaining a constant speed. Is there a net force on the car as it rounds the curve? (Q7-2) 1. 1. No – its speed is constant No – its speed is constant 2. Yes 2. Yes 3. It depends on the sharpness of the curve and the speed of the car 3. It depends on the sharpness of the curve and the speed of the car 4. No – its curve isn’t horizontal. 4. No – its curve isn’t horizontal. 1 It’s hearsay… You may have heard that the force that pushes you to the right side of the car when making a left hand turn is called the centrifugal force. This is a myth that must be busted! The centriFugal Force is a Fictitious Force! 2 Centripetal Acceleration: Equation 2 2 " d % " 2(r % $ ' $ ' v 2 # t & # T & 4( 2 r ac = = = = 2 r r r T Centripetal Acceleration: Period The centripetal acceleration has to do with the period of the spin. Period (T): the time it takes for one object to complete one full rotation or revolution Remember one full revolution or rotation is either 360o or 2π radians 4" 2 r ac = 2 T ! Centripetal acceleration = 4 x pi squared x the radius divided by the period squared ! Linear/tangential velocity (m/s) Example: A child 1.35 m from the center of a merry-go-round is moving with a period of 2 minutes. What is her centripetal acceleration in m/sec2? 4" 2 r= 4" (1.35) ac = 2 ) # 60 sec &, T +2 min% (. 2 2 * ! ! = 0.0037 m s2 $ 1min '- ! ΣF = m ac F centripetal = F friction On a day when the roads are icy, the coefficient of friction between a typical tire and the pavement is 0.200. What is the maximum speed a car can make a turn of radius 200.m? mv 2 = µ mg R v2 = µ g R v = µ g R = (0.2)(9.8)(200) v = 19.8 m / s 3 Roads can be banked, to reduce the need for friction to make a turn. N Take a cross section of the road… If a car of mass, m, is going to drive at a linear velocity, v, on a road. At what angle, θ, must the road be banked? N N cos θ X N sin θ Banked turns N cos θ X θ N sin θ θ "Fy = 0 θ From the y axis.. ! ΣFy = 0 r r N cos" ! mg = 0 θ mg From the x axis.. r r mg N= cos ! & mg # mv 2 $$ cos ' !! sin ' = R % " r v2 g tan ! = R v2 tan ! = r gR A girl on a merry-go-round is standing 5 m from the center, and holds a yoyo. If the string makes an angle of 3o with the vertical, how fast is she going? Note that the banking angle does not depend upon mass. r "F y Tcos3 v2 tan ! = r gR mg r mv 2 N sin ! = R r T X 3o =0 r r T cos # ! mg = 0 r mgr T= cos! Tsin3 mg 4 A girl on a merry-go-round is standing 5 m from the center, and holds a yoyo. If the string makes an angle of 3o with the vertical, how fast is she going? r r o ! F = T sin 3 x 3o mv 2 r v2 R g tan 3o = R mv 2 = r mg sin 3o = cos 3o R Tsin3 A daredevil drives a motorcycle on a loop-the-loop track. What is the slowest he can go and still make it? (R = 4.0m) 4m r r v = Rg tan 3o r v = 5(9.8) tan 3o = 1.6 m / s Remember, that mg is constant, but the normal force varies with the speed. Of course the tricky part is at the top. Radius = 4.0 m "F = ma c r r mg + N = mac 0 N mg N mg ! ! r mv 2 mg = R r 2 v = gR r v = gR = (9.8)(4) = 6.26 m / s HIDDEN So why aren’t real loop-theloop tracks circular? A ball moves at a constant speed along a horizontal circle inside a friction-free cone. The weight of the ball is mg. What other significant force(s) act on the ball? What is the direction of the net force on the ball? N mg This is the unbalanced force that is the centripetal force. 5 A rider in a amusement park ride finds herself stuck with her back to the carpeted wall. Which diagram correctly shows the forces acting on her? Lift 1 2 mg 3 4 5 Floor Q A rider in a amusement park ride finds herself stuck with her back to the carpeted wall. Which diagram correctly shows the forces acting on her? Friction Q7-4 Normal Force 1 2 3 4 5 (Centripetal Force) Floor mg 6

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Download PDF

advertising