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## PowerPoint Slideshow about ' Centripetal Force' - tatum-vaughan

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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.

dq

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.

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 SawLaw 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 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 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 m/s.

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

q

FT

r

mgtan q

mg

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 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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