Transcription of Linear and Angular Velocity Examples
1 Linear and Angular Velocity Examples Example 1 Determine the Angular displacement in radians of revolutions. Round to the nearest tenth. Each revolution equals 2 radians. For revolutions, the number of radians is 2 or 13. 13 radians equals about radians. Example 2 Determine the Angular Velocity if revolutions are completed in 4 seconds. Round to the nearest tenth. The Angular displacement is 2 or radians. = t = = , t = 4 Use a calculator. The Angular Velocity is about radians per second. Example 3 AMUSEMENT PARK Jack climbs on a horse that is 12 feet from the center of a merry-go-round. The merry-go-round makes 314 rotations per minute. Determine Jack s Angular Velocity in radians per second. Round to the nearest hundredth. The merry-go-round makes 314 or revolutions per minute.
2 Convert revolutions per minute to radians per second. revolutions1 minute 1 minute60 seconds 2 radians1 revolution radian per second Jack has an Angular Velocity of about radian per second. Example 4 Determine the Linear Velocity of a point rotating at an Angular Velocity of 12 radians per second at a distance of 8 centimeters from the center of the rotating object. Round to the nearest tenth. v = r v = (8)(12) r = 8, = 12 v Use a calculator. The Linear Velocity is about centimeters per second. Example 5 Refer to the application in Example 3. Determine Jack s Linear Velocity . v = r v (12)( ) r = 12, = v Use a calculator. Jack s Linear Velocity is about feet per second. Example 6 BICYCLES The tires on a bicycle have a diameter of 24 inches. If the tires are turning at a rate of 50 revolutions per minute, determine the bicycle s speed in miles per hour (mph).
3 If the diameter is 24 inches, the radius is 12 inches. This measure needs to be written in miles. The rate needs to be written in hours. v = r v = 12 in. 1 ft12 in. 1 mi5280 ft 50 rev1 min 21 rev 60 min1 h v Use a calculator. The speed of the bicycle is about miles per hour.
