# Centripetal Force - PowerPoint PPT Presentation

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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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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.

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.

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.

### 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

### 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

• 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

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

q

FT

r

mgtan q

mg

### 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°