Circular Motion Relationships | Show Me The Physics

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Diagram of an object moving in a circle with an incorrectly drawn acceleration vector

What's wrong with this picture?

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Acceleration Vector should be directed towards center

Kinematics in 2D

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B. Factors Affecting Centripetal Acceleration

1. Velocity and Acceleration?

Equation:

a_c = V² / r

Direct Square Relationship (Both variables on top, one is squared)

V	a
x 2	x 4
x 3	x 9
x 4	x 16
x 1/2	x 1/4
x 1/4	x 1/16

2. Acceleration and Radius?

Equation:

a_c = V² / r

Man swinging a remote-control car in a circle

Inverse Relationship

(One variable on top, other on bottom)

a	r
x 1/2	x 2
x 1/3	x 3
x 1/4	x 4
x 4	x 1/4
x 2	x 1/2

C. More Word Problems

Given

A 2.0 kg cart travels in a horizontal circle at a constant speed of 6.0 m/s.
If the r of circle is 3.0 m, what is centripetal acceleration?

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a_c = V² / r
= (6.0 m/s)² / 3.0 m

a_c = 12 m/s²

Challenge

Given

Calculate the speed an earth satellite must have to maintain a circular orbit at an altitude of 2.0 x 10⁵ m (200,000 m) where the acceleration due to gravity is 9.2 m/s² (radius of earth is 6,400,000 m)

[ Flash ]

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r = 6,400,000 m + 200,000 m

r = 6,600,000 m

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a_c = V² / r

9.2 m/s² = V² / (6,600,000 m)

9.2 m/s²(6,600,000 m) = V²

V = 7,792 m/s

or 7800 m/s (correct significant digits)

Non-uniform Circular Motion

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