A wheel starts from rest and has an angular acceleration of 4.0 rad/s^(2). When it has made 10 rev its angular velocity is:

22.41 rad/s

wf^2=wi^2+2ad

d= 10*2PI

Zero

To find the angular velocity of the wheel after it has made 10 revolutions, you can use the equation that relates angular acceleration, angular velocity, and time:

ω = ω₀ + αt

Where:
ω is the final angular velocity
ω₀ is the initial angular velocity (in this case, 0 because the wheel starts from rest)
α is the angular acceleration (given as 4.0 rad/s^2)
t is the time taken to reach the final angular velocity (which we need to find)

Since the wheel starts from rest, its initial angular velocity ω₀ is 0. We need to find the time t it takes for the wheel to make 10 revolutions.

Since 1 revolution is equal to 2π radians, 10 revolutions is equal to 20π radians. Therefore, our final angular displacement θ is 20π radians.

To find the time t, we can use the formula for angular displacement:

θ = ω₀t + 0.5αt²

Since ω₀ is 0 in this case, the equation simplifies to:

θ = 0.5αt²

Plugging in the values, we have:

20π = 0.5 * 4.0 * t²

Now, we can solve for t:

t² = (20π) / (0.5 * 4.0)
t² = 10π

Taking the square root of both sides, we get:

t ≈ √(10π)

Using a calculator, we find that t ≈ 5.02 seconds.

Now, we can substitute this value of t into the original equation to find the final angular velocity ω:

ω = ω₀ + αt
ω = 0 + 4.0 * 5.02

Simplifying, we get:

ω ≈ 20.08 rad/s

Therefore, when the wheel has made 10 revolutions, its angular velocity is approximately 20.08 rad/s.

8.9