Arc Lengths Sectors and Rotational Speeds Dr Shildneck

Arc Lengths, Sectors, and Rotational Speeds Dr. Shildneck Fall, 2015

• Recall from the definition, the formula for a radian, is the arc length divided by the radius. This formula will allow us to solve problems that involve the radius, arc length, and central angle (in radians). Definition of Radians multiply by r divide by θ Note: These formulas only work if the angle is in radian measure. Arc Length

EXAMPLE 1 On a circle with radius 9 inches, find the length of the arc intercepted by a central angle of radians.

EXAMPLE 2 On a circle with radius 10 cm, find the length of the arc intercepted by a central angle of 220 o.

EXAMPLE 3 For a circle with radius 11 cm, find the area of the sector created by a central angle of radians.

• There are three types of speeds that we will discuss regarding the rotation around an axis (central point). • Think about the different ways we might measure speeds while you are riding a carrousel. Rotational Speeds

• Think of linear speed as how far you travel around in a circle as you go around in a certain amount of time. • Think of angular speed as how many degrees or radians you rotate around the center of the circle as you go around in a certain amount of time. • Think or rotational or revolutionary speed as how many times you go around in a specific amount of time. Rotational Speeds

EXAMPLE 4 A second hand on a clock is 15 cm long. Find the angular speed (in degrees per second) and the linear speed (in cm/sec) at the arrow at the tip of the second hand.

EXAMPLE 5 A carousel is rotating at a rate of 6 revolutions per minute. Billy is sitting on a horse on the outside, 25 feet from the center of the ride. Hannah is sitting on an innermost horse, 15 feet from the center. Find the angular (degrees per minute) and linear speeds (feet per minute) of both riders.

• P. 238 #27 -53 odd • Practice Degree-Radian Timed Quiz ASSIGNMENT