Question

A cyclist is riding a bicycle whose wheels have a diameter of 2.1 feet. Suppose the wheels turn at a rate of 260 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.1633rad/min

b.1715feet/min

Explanation:

We are given that

Diameter of wheel, d=2.1 feet

Radius of wheel, r=
`(d)/(2)=(2.1)/(2)`feet

Rate=260 rev/min

a. We have to find the angular speed of the wheel in rad/min

1 rev=
`2\pi`radian

Where
`\pi=3.14`

Using the value

Angular speed=
`260* 2* 3.14/min`

Angular speed,
`\omega=1633rad/min`

(b)

Speed=
`r\omega`

Using the formula

Speed of the cyclist=
`(2.1)/(2)* 1633`feet/min

Speed of the cyclist=1714.65
`\approx 1715`feet/min