Question

A child's first bicycle has 12-inch tires. These tires have a 6-inch radius. How fa r does the bicycle move forward each time the wheel makes one complete rotation? Give your answer in meters. (1 inch = 0.022 meters) b. A woman's ten-speed bicycle has 27-inch tires (13.5-inch radius). How far does this bicycle …

Answer 1

a. s = 0.96 m

b. s = 2.15 m

Step-by-step explanation:

a.

The relationship between the linear displacement and the angular displacement is given as follows:

`s = r\theta`

where,

s = linear distance covered = ?

r = radius of wheel = (6 in)(0.0254 m/1 in) = 0.1524 m

θ = angular displacement = (1 rev)(2π rad/1 rev) = 2π rad

Therefore,

`s = (0.1524\ m) 2\pi`

s = 0.96 m

b.

Assuming, we have to find linear displacement here, as well:

`s = r\theta`

where,

s = linear distance covered = ?

r = radius of wheel = (13.5 in)(0.0254 m/1 in) = 0.3429 m

θ = angular displacement = (1 rev)(2π rad/1 rev) = 2π rad

Therefore,

`s = (0.3429 \ m) 2\pi`

s = 2.15 m