A particle with constant speed is moving around the circle f

A particle with constant speed is moving around the circle from point P to point R in 16 seconds. The radius of the circle is 62 feet, and the measure of the central angle is 275 degree a. Find the length of the arc from P to R to the nearest foot. b. Find the linear velocity to the nearest foot per second. c. Find the angular velocity to the nearest tenth of a radian per second.

Solution

a) arc length = 2pi R ( C / 360)

plugging the values we get

2pi * 62 ( 275 / 360 )

= 297 feet

c) converting 275 degrees to radians

275 degrees = 4.797 radians

angular velocity = 4.797/16 = 0.2998 radians / sec

b) linear velocity = angular velocity * radius

= 0.2998 * 62

= 18.59 feet / sec