Question

A cyclist is riding a bicycle whose wheels have a diameter of feet. Suppose the wheels turn at a rate of revolutions per minute.

(a) Find the angular speed of the wheels in radians per minute.
(b) Find the speed of the cyclist in feet per minute. Do not round any intermediate computations, and round your answer to the nearest whole number.

Answer 1

a.2010 rad/min

b.2412 feet/min

Explanation:

We are given that

Diameter of wheel,d=2.4 feet

Radius,r=
`(d)/(2)=(2.4)/(2)=1.2feet`

a.Rate=320 rev/minute

1 rev=
`2\pi` radian

320 rev/minute=
`320* 2\pi=640\pi radian/minute`

Where
`\pi=3.14`

Angular speed=
`640* 3.14=2010 rad/min`

b.Speed,v=
`r\omega`

`v=2010* 1.2=2412 feet/min`