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Radian application Problems

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

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Radian application Problems

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

  2. Angular and Linear Velocity Angular Velocity- the # of degrees per unit of time Linear Velocity-distance per unit of time

  3. 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

  4. 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. If θ is in radians and ω is in radians per unit of time, then ω=(revolutions/rotations)θ

  5. Formulas for linear velocity Linear Velocity v, of a point on a rotating object is the distance the point travels along its circular path per unit of time. If θ is in radians and ω is in radians per unit of time, then v=rω

  6. 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? Calculate the angle Substitute θ=2π and t=10 seconds into ω=θ/t 3)Convert the angular speed from radians per second to radians per minute.

  7. . Example 2 A 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

  8. 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?

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