Centripetal ForceAcceleration in a CircleCentripetal AccelerationBuzz SawLaw of Acceleration in CirclesConical PendulumRadial Net ForceAcceleration to VelocityPeriod of RevolutionRadial TensionCentripetal ForceCentripetal ForceAcceleration in a CircleAcceleration in a CirclevdAcceleration is a vector Acceleration is a vector change in velocity compared change in velocity compared to time.to time.For small angle changes the For small angle changes the acceleration vector points acceleration vector points directly inward.directly inward.This is called This is called centripetalcentripetal acceleration.acceleration.a1vd2vCentripetal AccelerationCentripetal AccelerationUniform circular motion takes place with a constant Uniform circular motion takes place with a constant speed but changing velocity direction.speed but changing velocity direction.The acceleration always is directed toward the center The acceleration always is directed toward the center of the circle and has a constant magnitude.of the circle and has a constant magnitude.rrvar22Buzz SawBuzz SawA circular saw is designed A circular saw is designed with teeth that will move at with teeth that will move at 40. m/s.40. m/s.The bonds that hold the The bonds that hold the cutting tips can withstand a cutting tips can withstand a maximum acceleration of maximum acceleration of 2.0 x 102.0 x 1044 m/s m/s22..Find the maximum diameter Find the maximum diameter of the blade.of the blade.Start with Start with aa = = vv22//rr..•rr = = vv22//aa..Substitute values:Substitute values:•rr = (40. m/s) = (40. m/s)22/(2.0 x 10/(2.0 x 1044 m/s m/s22))•rr = 0.080 m. = 0.080 m.Find the diameter:Find the diameter:•dd = 0.16 m = 16 cm. = 0.16 m = 16 cm.Law of Acceleration in Law of Acceleration in CirclesCirclesMotion in a circle has a Motion in a circle has a centripetal acceleration.centripetal acceleration.There must be a There must be a centripetal centripetal forceforce..•Vector points to the center Vector points to the center The The centrifugalcentrifugal force that we force that we describe is just inertia.describe is just inertia.•It points in the opposite It points in the opposite direction – to the outsidedirection – to the outside•It isn’t a real force It isn’t a real force aFrmrmvFr22Conical PendulumConical PendulumA 200. g mass hung is from a 50. cm string as a A 200. g mass hung is from a 50. cm string as a conical pendulum. The period of the pendulum in a conical pendulum. The period of the pendulum in a perfect circle is 1.4 s. What is the angle of the perfect circle is 1.4 s. What is the angle of the pendulum? What is the tension on the string?pendulum? What is the tension on the string?FTRadial Net ForceRadial Net ForceThe mass has a downward The mass has a downward gravitational force, -gravitational force, -mgmg..There is tension in the string.There is tension in the string.•The vertical component must The vertical component must cancel gravitycancel gravityFFTyTy = = mgmgFFTT = = mgmg / cos / cos FFTrTr = = mgmg sin sin / cos / cos = = mgmg tan tan This is the net radial force – the This is the net radial force – the centripetal force.centripetal force.mgFTFT cos FT sin Acceleration to VelocityAcceleration to VelocityThe acceleration and The acceleration and velocity on a circular path velocity on a circular path are related.are related.mgFTmg tan tantan/tan/22grvgrvrvagmFarPeriod of RevolutionPeriod of RevolutionThe pendulum period is The pendulum period is related to the speed and related to the speed and radius.radius.FTmg tan rLgTgLTLgrvTLTrvLr22222224/coscos/sinsin/sin4tan/sin2/2sinLcos = 0.973 = 13°Radial TensionRadial TensionThe tension on the string can be found using the The tension on the string can be found using the angle and mass.angle and mass.FFTT = = mgmg / cos / cos = 2.0 N = 2.0 NIf the tension is too high the string will break!If the tension is too high the string will
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