Radian application Problems
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Transcript of Radian application Problems
Radian application ProblemsWhat is angular speed? How is it used to solve problems? What t is linear speed?
Angular and Linear VelocityAngular Velocity- the # of degrees per unit of time
Linear Velocity-distance per unit of time
Variable Key
r=radians a= arc =angle through which the point
rotates (usually in radians, but not always)
v= linear velocity, in distance per time =angular velocity (often in radians
per unit of time) t= length of time to rotate through a
particular angle
Formulas for angular velocity
Angular velocity of a point on a rotating object is the # of (degrees/radians/revolutions) through which the point turns per unit of time.
t
If is in radians and is in radians θ ωper unit of time, then
ω=(revolutions/rotations) θ
Formulas for linear velocity
If is in radians and is in radians θ ωper unit of time, then
v=rω
Linear Velocity v, of a point on a rotating object is the distance the point travels along its circular path per unit of time.
tav
Example 1: A lighthouse in the middle of a channel rotates
its light in a circular motion with constant speed. If the beacon of light completes 1 rotation every 10 seconds, what is the angular speed of the beacon in radians per minute?
uteradiansuteonds
ondsradiansonds
radians
min/12min1sec60
sec10)(2
sec10)(2
2
1) Calculate the angle
2) Substitute θ=2π and t=10 seconds into ω=θ/t
3)Convert the angular speed from radians per second to radians per minute.
Example 2A Ferris Wheel rotates 3 times each minute. The passengers sit in seats that are 25 feet from the center of the wheel. What is the angular velocity of the wheel in degrees per minute and radians per minute?
3 revolutions per minute is
.
uteradiansuteper min/623min10803603
CW Problems
1)Consider the earth which rotates on its axis once every 24 hours. If one rotation of the earth is 2π. What is the angular velocity of the earth in degrees per hour?
2)A ceiling fan rotates 30 times per minute. What is the fans angular velocity in radians per minute?
perhourhourradians
151224
2
60230