Question

A wheel revolving at 6 rev/s has an angular acceleration of 4 rad/s². Find the number of turns the wheel must make to acquire an angular speed of 26 rev/s.

A. 18
B. 19
C. 20
D. 21
E. 22

Answer 1

The wheel must make 23 turns to acquire an angular speed of 26 rev/s.

How can you find the number of turns the wheel must make to acquire an angular speed of 26 rev/s?

ω² = ω₀² + 2αθ

where:

ω is the final angular speed (26 rev/s)

ω₀ is the initial angular speed (6 rev/s)

α is the angular acceleration (4 rad/s²)

θ is the number of turns (in radians)

First, we need to convert the angular speeds from revolutions per second to radians per second:

ω₀ = 6 rev/s * (2π rad/rev) = 12π rad/s

ω = 26 rev/s * (2π rad/rev) = 52π rad/s

Now, we can plug the values into the equation:

52π² = 12π² + 2(4 rad/s²)θ

Solving for θ, we get:

θ = (52π² - 12π²) / (2 * 4 rad/s²) ≈ 45π rad

Finally, we convert the number of turns from radians to revolutions:

45π rad * (1 rev/2π rad) ≈ 22.5 rev

Since the number of turns must be a whole number, we round up to the nearest integer. Therefore, the wheel must make 23 turns to acquire an angular speed of 26 rev/s.