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

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Presentation transcript:

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

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

Variable KeyVariable 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 velocityFormulas 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

Formulas for linear velocityFormulas for linear velocity If θ is in radians and ω is in radians per 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.

Example 1: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? 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 2Example 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.

CW ProblemsCW 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?