A cyclist starts from rest and pedals such that the wheels of his bike have a constant angular acceleration. After 18.0 s, the wheels have made 190 rev. What is the angular acceleration of the wheels?

What is the angular velocity of the wheels after 18.0 s?

If the radius of the wheel is 34.0 cm, and the wheel rolls without slipping, how far has the cyclist traveled in 18.0 s?

use 1/2alphat^2=2pi*revolutions to find alpha then use wf=wi+alpha(t) to find the final angular velocity

x=wrt

To find the angular acceleration of the wheels, we can use the formula:

angular acceleration (α) = (final angular velocity (ω) - initial angular velocity (ω0)) / time (t)

In this case, the initial angular velocity is 0 since the cyclist starts from rest, and the final angular velocity can be found using the formula:

final angular velocity (ω) = (number of revolutions (N) * 2π) / time (t)

Given that the number of revolutions is 190 and the time is 18.0 seconds, we can substitute these values into the formula to find the final angular velocity:

ω = (190 rev * 2π) / 18.0 s

Now we can substitute the values of ω and ω0 into the formula for angular acceleration to find the answer to the first question:

α = (ω - ω0) / t

To find the angular velocity of the wheels after 18.0 seconds, substitute the values into the formula for ω:

ω = (190 rev * 2π) / 18.0 s

To find the distance the cyclist has traveled in 18.0 seconds, we can use the formula:

distance (d) = (number of revolutions (N) * circumference of the wheel)

The circumference of the wheel can be found using the formula:

circumference = 2π * radius

Given that the radius of the wheel is 34.0 cm, substitute the values into the formula for the circumference:

circumference = 2π * 34.0 cm

Now we can substitute the values of N and the circumference into the formula for distance to find the answer to the third question:

d = (190 rev * 2π * 34.0 cm) / (1 rev)