Question

A bicycle with wheels 28 inches in diameter is traveling at the rate of 5 feet per second.

The angular speed of the wheels is_____radians/second and the tires
make____rotations per second. Round your answers to 2 decimal
places. Also be sure to use the same units when calculating your answers.

Answer 1

Step-by-step explanation:

Because the velocity is in feet per second, we will change the circumference of the wheel to feet as well.

C = πd so

C = 3.1415(28)

C = 87.9646 inches *
`(1ft)/(12in)` = 7.3304 ft in 1 revolution

Angular velocity is

ω =
`(v)/(r)` where r is the radius of the wheel. We know that this wheel travels 7.3304 in 1 revolution, and 1 revolution is equal to 2pi, so

ω =
`(5ft)/(sec)*(2\pi )/(7.3304ft)=4.29(radians)/(sec)`. That's how fast the angle of the wheel is changing.

As far as the rotations or revolutions per second goes,

`(5ft)/(sec)*(1rev)/(7.3304ft)=.68(rev)/(sec)`