In a circle of radius 90 cm, an arc 186 cm long subtends

1. In a circle of radius 90 cm, an arc 186 cm long subtends an angle of how many radians? How many degrees?

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2.In a circle with a 119 ft radius, how long is an arc associated with an angle of 
5.1 radians?

3. A flywheel with a diameter of 14 cm is rotating at a rate of 9 radians per second. What is the linear speed of a point on its rim, in centimeters per minute?

4.  When Brett and Will ride the carousel, Brett always selects a horse on the outside row, whereas Will prefers the row closest to the center. These rows are 20ft 10 in. and 12ft 5in. 
from the center, respectively. The angular speed of the carousel is 2.9 revolutions per minute. What is the difference, in miles per hour, in the linear speeds of Brett and Will?

5. A rider in a road bike race had an average linear speed of 40.672 km/hr. The wheel of his bicycle had a diameter of 67 cm. What is his angular speed, in revolutions per hour?

6. The rear wheel of a tractor has a 23-in radius. Find the angle (in radians) through which a wheel rotates in 15 sec if the tractor is traveling at a speed of 24mph.

 

7. One gear wheel turns another, the teeth being on the rims. The wheels have 10 cm and 20 cm radii, and the smaller wheel rotates at 30 mph. Find the angular speed of the larger wheel, in radians per second.

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