Centripetal Acceleration

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51 **

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Centripetal Acceleration

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(a) Is an object moving in a circle with constant speed accelerating?

(b) What is the acceleration of the moon around earth if the period of the moon's path around earth is

27(1/3) days, and the distance of the moon from the earth is 240,000 miles?

**The string**:

(a) S_{7}P_{5}A_{51} (Linear Motion).
**The math**:

(a) The Pj Problem of Interest (PPI) is of type *change*. Problems of speed, velocity, acceleration and duration are *change problems*.

Newton's first law of motion states that an object remains at rest if it is at rest or it moves with constant speed in linear motion if it is in motion, unless a force acts on it to change its state.

Newton's second law of motion indicates that the force that changes the linear motion of an object is equal to the product of its mass and acceleration

So, an object in circular motion does accelerate. This acceleration is called *cetripetal acceleration* and is given by:

v^{2}/r (where v is the constant speed and r is the radius of the circular path).

(b) Distance of earth to moon 240,000 miles = 240,000 x 5280 = 1.27 x 10^{9} ft.

Circumference of moon's path = 2πr = 2π(240,000 x 5280) = 2π(1.27 x 10^{9}) ft

Time it takes moon to complete one revolution around earth

= 27(1/3) days = (27.33 x 24 x 3600) = 2.36 x 10^{6} secs

So, moon's speed around the earth, v = [2π(1.27 x 10^{9})]/(2.36 x 10^{6})

approximately = 3.30 x 10^{3} ft/sec

So, acceleration of moon around earth:

= v^{2}/r

= (10.89 x 10^{6})/(1.27 x 10^{9}) = 8.6 x 10^{-3}
= 0.0086 ft/sec^{2} approximately.

The *point* "**.**" is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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