Circles and Ellipses for Physics Help

Introduction

Let’s get into plane curves. In some ways, the following formulas are easier for mathematicians to derive than the ones for figures consisting of lines and angles; in other ways, the formulas for curves are more troublesome. Fortunately, however, we’re physicists, and the mathematicians have done all the work for us. All we need to do is take note of the formulas and apply them to situations as the needs arise.

Perimeter Of Circle

Suppose that we have a circle having radius r , as shown in Fig. 4-33. Then the perimeter B , also called the circumference , of the circle is given by the following formula:

B = 2π r

Fig. 4-33 Perimeter and area of a circle.

Interior Area Of Circle

Suppose that we have a circle as defined above and in Fig. 4-33. The interior area A of the circle can be found using this formula:

A = π r ²

Fig. 4-33 Perimeter and area of a circle.

Perimeter Of Ellipse

Suppose that we have an ellipse whose major half-axis measures r and whose minor half-axis measures s , as shown in Fig. 4-34. Then the perimeter B of the ellipse is given approximately by the following formula:

Fig. 4-34 Perimeter and area of an ellipse.

B ≈ 2π [( r ² + s ² )/2] ^1/2

Interior Area Of Ellipse

Suppose that we have an ellipse as defined above and in Fig. 4-34. The interior area A of the ellipse is given by

A = π rs

Fig. 4-34 Perimeter and area of an ellipse.

Practice problems for these concepts can be found at:  Basics Of Geometry for Physics Practice Test