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Centripetal Force

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Acceleration in a Circle Acceleration is a vector change in velocity compared to time. For small angle changes the acceleration vector points directly inward. This is called centripetal acceleration. dd

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Centripetal Acceleration Uniform circular motion takes place with a constant speed but changing velocity direction. The acceleration always is directed toward the center of the circle and has a constant magnitude.

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Buzz Saw A circular saw is designed with teeth that will move at 40. m/s. The bonds that hold the cutting tips can withstand a maximum acceleration of 2.0 x 10 4 m/s 2. Find the maximum diameter of the blade. Start with a = v 2 / r. r = v 2 /a. Substitute values: r = (40. m/s) 2 /(2.0 x 10 4 m/s 2 ) r = 0.080 m. Find the diameter: d = 0.16 m = 16 cm.

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Law of Acceleration in Circles Motion in a circle has a centripetal acceleration. There must be a centripetal force. Vector points to the center The centrifugal force that we describe is just inertia. It points in the opposite direction – to the outside It isn’t a real force

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Conical Pendulum A 200. g mass hung is from a 50. cm string as a conical pendulum. The period of the pendulum in a perfect circle is 1.4 s. What is the angle of the pendulum? What is the tension on the string? FTFT

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Radial Net Force The mass has a downward gravitational force, -mg. There is tension in the string. The vertical component must cancel gravityThe vertical component must cancel gravity F Ty = mg F T = mg / cos F Tr = mg sin / cos = mg tan This is the net radial force – the centripetal force. mg FTFT F T cos F T sin

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Acceleration to Velocity The acceleration and velocity on a circular path are related. mg FTFT mg tan r

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Period of Revolution The pendulum period is related to the speed and radius. FTFT mg tan r L cos = 0.973 = 13 °

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Radial Tension The tension on the string can be found using the angle and mass. F T = mg / cos = 2.0 N If the tension is too high the string will break! next

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