Exploring Arc Length and Circular Motion

This lesson covers the concept of arc length and its relation to central angles in geometry. It explains how to calculate arc length using the radius and angle in radians, and provides example problems to illustrate these calculations. The lesson also introduces linear and angular velocity, demonstrating how to compute these using real-world examples. Additionally, it covers the area of a sector and how to calculate distances between cities using arc length. The lesson concludes with a free response question to reinforce the concepts learned.

What is the formula for calculating arc length?

• Arc length = radius / angle in radians

• Arc length = radius - angle in radians

• Arc length = radius + angle in radians

• Arc length = radius x angle in radians

How do you convert degrees to radians?

• Divide by 180 and multiply by π

• Divide by π and multiply by 180

• Multiply by 180 and divide by π

• Multiply by π and divide by 180

What is the relationship between the measure of angles and the lengths of arcs they subtend?

• There is no relationship

• They are equal

• They are directly proportional

• They are inversely proportional

What is the relationship between linear velocity, arc length, and time?

• Linear velocity = arc length x time

• Linear velocity = arc length / time

• Linear velocity = time / arc length

• Linear velocity = arc length + time

What unit is used to measure angular velocity?

• Degrees per minute

• Revolutions per minute

• Miles per hour

• Radians per second

How is angular velocity represented in physics?

• Using the Greek letter alpha (α)

• Using the letter V

• Using the letter A

• Using the Greek letter omega (Ω)

How do you calculate the distance between two points on Earth given their latitudes?

• Use the formula s = rθ, converting the difference in latitudes to radians

• Multiply the difference in latitudes by the radius of the Earth

• Subtract the two latitudes and multiply by the radius of the Earth

• Add the two latitudes and divide by the radius of the Earth

What is the exact length of an angle measure of one minute on Earth?

• Exactly 101 feet

• Approximately 1.15 miles

• Exactly 1 mile

• Approximately 0.01919 miles

What is the formula to find the area of a sector?

• Area = 1/2 * radius^2 * angle in radians

• Area = radius * angle in radians

• Area = 2 * radius * angle in radians

• Area = radius^2 / angle in radians

How do you convert an angle from minutes to decimal degrees?

• Subtract 60

• Multiply by 60

• Add 60

• Divide by 60