Earth's Motion and Arc Length

The video tutorial explains how to calculate the length of an arc in a circle using the formula S = R x THETA, where the angle must be in radians. It demonstrates converting degrees to radians and simplifies the calculation for a circle with a radius of 3 cm and a central angle of 120 degrees. The tutorial then applies this concept to an application problem involving the Earth's orbit around the Sun, assuming a circular path with a radius of 93 million miles. The video concludes by calculating the distance the Earth travels in one month, approximately 48.7 million miles.

What is the radius of the circle in the initial problem?

• 5 centimeters

• 3 centimeters

• 2 centimeters

• 4 centimeters

What is the central angle in degrees for the initial arc length problem?

• 100 degrees

• 120 degrees

• 90 degrees

• 150 degrees

What is the formula for calculating arc length?

• S = R + THETA

• S = R x THETA

• S = R / THETA

• S = R - THETA

How do you convert degrees to radians?

• Multiply by 180/pi

• Multiply by pi/180

• Divide by pi

• Divide by 180

What is the arc length of the circle with a radius of 3 cm and a central angle of 120 degrees?

• 2 cm

• 3 cm

• 4 cm

• 6.28 cm

What is the assumed shape of Earth's path around the Sun in the application problem?

• Triangle

• Square

• Ellipse

• Circle

What is the radius of Earth's orbit around the Sun in the application problem?

• 80 million miles

• 100 million miles

• 70 million miles

• 93 million miles

What fraction of a revolution does Earth complete in one month?

• 1/4

• 1/8

• 1/12

• 1/6

What is the value of theta used for calculating Earth's travel distance in one month?

• pi/2

• pi/4

• pi/3

• pi/6

Approximately how many million miles does Earth travel in one month?

• 50 million miles

• 48.7 million miles

• 60 million miles

• 45 million miles