Radian application Problems

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Radian application Problems What is angular speed? How is it used to solve problems? What t is linear speed?

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Radian application Problems. What is angular speed? How is it used to solve problems? What t is linear speed?. Angular and Linear Velocity. Angular Velocity- the # of degrees per unit of time. Linear Velocity-distance per unit of time. Variable Key. r=radians a= arc - PowerPoint PPT Presentation

Transcript of Radian application Problems

Page 1: Radian application Problems

Radian application ProblemsWhat is angular speed? How is it used to solve problems? What t is linear speed?

Page 2: Radian application Problems

Angular and Linear VelocityAngular Velocity- the # of degrees per unit of time

Linear Velocity-distance per unit of time

Page 3: Radian application Problems

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

Page 4: Radian application Problems

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

Page 5: Radian application Problems

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

Page 6: Radian application Problems

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.

Page 7: Radian application Problems

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

Page 8: Radian application Problems

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