Centripetal force
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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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Acceleration in a circle
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


Centripetal acceleration
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.


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 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


Law of acceleration in circles
Law of Acceleration in Circles m/s.

  • 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


Conical pendulum
Conical Pendulum m/s.

  • 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


Radial net force
Radial Net Force m/s.

  • 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


Acceleration to velocity
Acceleration to Velocity m/s.

  • The acceleration and velocity on a circular path are related.

q

FT

r

mgtan q

mg


Period of revolution
Period of Revolution m/s.

  • The pendulum period is related to the speed and radius.

q

L

FT

r

mgtan q

cos q = 0.973

q = 13°


Radial tension
Radial Tension m/s.

  • 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!

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