To solve this problem, we need to use the equations of rotational motion.

Step 1: Convert the revolutions to radians
First, we need to convert the revolutions to radians because the angular speed is given in rad/s. We know that 1 revolution is equal to 2π radians. So, 2.50 revolutions is equal to 2.50 * 2π = 5π radians.

Step 2: Use the equation of motion
The equation of motion that relates final angular speed (ωf), initial angular speed (ωi), angular acceleration (α), and angular displacement (θ) is:

ωf^2 = ωi^2 + 2αθ

We can rearrange this equation to solve for α:

α = (ωf^2 - ωi^2) / (2θ)

Step 3: Substitute the values into the equation
Now we can substitute the given values into the equation:

α = ((22.0 rad/s)^2 - (12.4 rad/s)^2) / (2 * 5π rad)

Step 4: Calculate the acceleration
After calculating the above expression, we get the angular acceleration α.

This is the step-by-step solution to the problem.

Question

To solve this problem, we need to use the equations of rotational motion.

Step 1: Convert the revolutions to radians
First, we need to convert the revolutions to radians because the angular speed is given in rad/s. We know that 1 revolution is equal to 2π radians. So, 2.50 revolutions is equal to 2.50 * 2π = 5π radians.

Step 2: Use the equation of motion
The equation of motion that relates final angular speed (ωf), initial angular speed (ωi), angular acceleration (α), and angular displacement (θ) is:

ωf^2 = ωi^2 + 2αθ

We can rearrange this equation to solve for α:

α = (ωf^2 - ωi^2) / (2θ)

Step 3: Substitute the values into the equation
Now we can substitute the given values into the equation:

α = ((22.0 rad/s)^2 - (12.4 rad/s)^2) / (2 * 5π rad)

Step 4: Calculate the acceleration
After calculating the above expression, we get the angular acceleration α.

This is the step-by-step solution to the problem.

Knowee AI · Accepted Answer

To solve this problem, we need to use the equations of rotational motion.

Step 1: Convert the revolutions to radians
First, we need to convert the revolutions to radians because the angular speed is given in rad/s. We know that 1 revolution is equal to 2π radians. So, 2.50 revolutions is equal to 2.50 * 2π = 5π radians.

Step 2: Use the equation of motion
The equation of motion that relates final angular speed (ωf), initial angular speed (ωi), angular acceleration (α), and angular displacement (θ) is:

ωf^2 = ωi^2 + 2αθ

We can rearrange this equation to solve for α:

α = (ωf^2 - ωi^2) / (2θ)

Step 3: Substitute the values into the equation
Now we can substitute the given values into the equation:

α = ((22.0 rad/s)^2 - (12.4 rad/s)^2) / (2 * 5π rad)

Step 4: Calculate the acceleration
After calculating the above expression, we get the angular acceleration α.

This is the step-by-step solution to the problem.

The angular speed of a propeller on a boat increases with constant acceleration from 12.4 rad/s to 22.0 rad/s in 2.50 revolutions. What is the acceleration of the propeller?

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