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Centripetal Force

Centripetal Force. 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. d q. Centripetal Acceleration.

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Centripetal Force

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  1. Centripetal Force

  2. 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. dq

  3. 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.

  4. 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 104 m/s2. Find the maximum diameter of the blade. Start with a = v2/r. r = v2/a. Substitute values: r = (40. m/s)2/(2.0 x 104 m/s2) r = 0.080 m. Find the diameter: d = 0.16 m = 16 cm. Buzz Saw

  5. 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

  6. 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? q FT

  7. Radial Net Force • The mass has a downward gravitational force, -mg. • There is tension in the string. • The vertical component must cancel gravity • FTy = mg • FT = mg / cos q • FTr = mg sin q / cos q = mg tan q • This is the net radial force – the centripetal force. q FT cos q FT FT sin q mg

  8. Acceleration to Velocity • The acceleration and velocity on a circular path are related. q FT r mgtan q mg

  9. Period of Revolution • The pendulum period is related to the speed and radius. q L FT r mgtan q cos q = 0.973 q = 13°

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

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