sec 42C arc length area of sector and velocity.notebook
September 11, 2014
Arc Length of a Circle:
S = arc length
r = measure of radius
θ = measure of angle, in radians
Example:
Find the length of the intercepted arc in each circle with the given central angle measure and radius.
Round to the nearest tenth.
a.
b.
Example:
Find the central angle measure (in radians) of an arc of length 11 cm on a circle with a radius of 4 cm.
Example:
The second hand on a clock is 5 inches long. How far does the tip of the second hand move in 45 seconds?
Area of a Sector of a Circle:
A = Area
r = measure of radius
θ = measure of angle, in radians
sec 42C arc length area of sector and velocity.notebook
September 11, 2014
Find the length of the intercepted arc in each circle with the given central angle measure and radius. Round to the nearest tenth.
a. r = 4 in and θ = b. r = 7 cm and θ =
Example:
The area of a sector of a circle and the measure of its central angle are given. Find the radius of the circle.
Example 4:
A sprinkler on a golf course is set to spray water over
a distance of 75 feet and rotates through an angle of 135 o.
Find the area of the fairway watered by the sprinkler.
sec 42C arc length area of sector and velocity.notebook
Find the area of the sector of the circle.
Linear Velocity = v = arc length
time
Angular velocity = ω =
angle
time
Relationship between velocities:
v = rω
Example:
Find the angular and linear speeds of a DVD in if the disc rotates at a rate of 3.5 revolutions per second and has a radius of 120 mm.
Example:
A circular mobile above a baby's crib makes 5 revolutions per minute.
a) What is the angular speed of the mobile in radians per minute?
b) How fast is a toy 9 inches from the center traveling in feet per minute?
c) How fast is a toy 6 inches from the center traveling in feet per minute?
September 11, 2014
sec 42C arc length area of sector and velocity.notebook
September 11, 2014
Find the rotation in revolutions per minute given the angular speed and the radius given the linear speed and the rate of rotation.
a. ω = 104π rad/min
b. v = 553 in/min, 0.09 rev/min
A typical vinyl record has a diameter of 30 cm.
When played on a turn table, the record spins at 33 1/3 revolutions per minute.
a. Find the angular speed, in radians per minute, of a record as it plays. Round to the nearest tenth.
b. Find the linear speed at the outer edge of the record as it spins, in centimeters per second.
sec 42C arc length area of sector and velocity.notebook
September 11, 2014
Homework:
Read section 4­2 and
Do pgs. 238 & 239, #'s 29, 31­35 all, 37, 38, 46, 48, 49, 52, 53, 56 & 57