Question

A bicycle has wheels of 0.8 m diameter. The bicyclist accelerates from rest with constant acceleration to 22 km/h in 11.6 s. What is the angular acceleration of the wheels?

Answer 1

α = 1.32 rad/s²

Step-by-step explanation:

given,

diameter of the bicycle = 0.8 m

radius of the bicycle = 0.4 m

initial speed of the bicyclist,u = 0 m/s

final speed of the bicyclist,v = 22 Km/h = 22 x 0.278

= 6.12 m/s

time,t = 11.6 s

acceleration =
`(v-u)/(t)`

=
`(6.12-0)/(11.6)`

=0.53 m/s²

we know,

a = α r

`\alpha=(a)/(r)`

`\alpha=(0.53)/(0.4)`

α = 1.32 rad/s²

the angular acceleration of the wheels is equal to α = 1.32 rad/s²